hyperelliptic(.ncag).info

the classification of hyperelliptic varieties in dimensions 2, 3 and 4

hyperelliptic groups

Every finite group occurring as the holonomy group of a hyperelliptic variety in dimension $2$, $3$ or $4$, with its character table and the tangent representations it carries. The last three columns count those representations by dimension.

group$\#G$classesdim $2$dim $3$dim $4$
$\mathrm{C}_{2}$22123
$\mathrm{C}_{3}$33135
$\mathrm{C}_{2} \times \mathrm{C}_{2}$44·24
$\mathrm{C}_{4}$44149
$\mathrm{C}_{5}$55·11
$\mathrm{S}_3$63··3
$\mathrm{C}_{6}$661723
$\mathrm{C}_{7}$77··2
$\mathrm{D}_4$85·15
$\mathrm{C}_{2} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$88··2
$\mathrm{C}_{8}$88·26
$\mathrm{Q}_8$85··2
$\mathrm{C}_{4} \times \mathrm{C}_{2}$88·213
$\mathrm{C}_{3} \times \mathrm{C}_{3}$99·16
$\mathrm{C}_{9}$99··2
$\mathrm{C}_{10}$1010·13
$\mathrm{C}_{6} \times \mathrm{C}_{2}$1212·325
$\mathrm{C}_{12}$1212·427
$\mathrm{G}(3,4,2)$126··5
$\mathrm{A}_4$124··2
$\mathrm{S}_3 \times \mathrm{C}_2$126··7
$\mathrm{C}_{14}$1414··2
$\mathrm{C}_{15}$1515··1
$\mathrm{C}_{2} \times \mathrm{D}_4$1610··2
$\mathrm{C}_{8} \times \mathrm{C}_{2}$1616··4
$\mathrm{D}_4 \circ \mathrm{C}_4$1610··5
$(\mathrm{C}_4 \times \mathrm{C}_2) \rtimes \mathrm{C}_2$1610··2
$\mathrm{G}(8,2,3)$167··5
$\mathrm{C}_{4} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$1616··4
$\mathrm{G}(8,2,5)$1610··5
$\mathrm{C}_{4} \times \mathrm{C}_{4}$1616·19
$\mathrm{G}(4,4,3)$1610··2
$\mathrm{S}_3 \times \mathrm{C}_3$189··10
$\mathrm{C}_{18}$1818··2
$\mathrm{C}_{6} \times \mathrm{C}_{3}$1818·223
$\mathrm{C}_{10} \times \mathrm{C}_{2}$2020··1
$\mathrm{C}_{20}$2020··2
$\mathrm{C}_{3} \times \mathrm{Q}_8$2415··8
$\mathrm{C}_{24}$2424··4
$\mathrm{C}_{3} \times \mathrm{D}_4$2415··15
$\mathrm{S}_3 \times \mathrm{C}_4$2412··11
$(\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2$249··5
$\mathrm{C}_{6} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$2424··6
$\mathrm{C}_{2} \times \mathrm{A}_4$248··3
$\mathrm{C}_{12} \times \mathrm{C}_{2}$2424·126
$\mathrm{G}(3,8,2)$2412··3
$\mathrm{C}_{3} \times \mathrm{C}_{3} \times \mathrm{C}_{3}$2727··1
$\mathrm{Heis}(3)$2711··2
$\mathrm{C}_{30}$3030··3
$\mathrm{C}_{8} \times \mathrm{C}_{4}$3232··2
$\mathrm{C}_{4} \times \mathrm{C}_{4} \times \mathrm{C}_{2}$3232··3
$\mathrm{G}(8,4,5)$3220··1
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$3214··8
$\mathrm{G}(8,4,5) \times \mathrm{C}_2$3220··2
$(\mathrm{C}_4 \times \mathrm{C}_4) \rtimes \mathrm{C}_2$3220··1
$\mathrm{G}(3,4,2) \times \mathrm{C}_3$3618··10
$\mathrm{S}_3 \times \mathrm{C}_6$3618··20
$\mathrm{C}_{6} \times \mathrm{C}_{6}$3636·123
$\mathrm{C}_{12} \times \mathrm{C}_{3}$3636··7
$\mathrm{C}_{20} \times \mathrm{C}_{2}$4040··1
$\mathrm{C}_{24} \times \mathrm{C}_{2}$4848··2
$\mathrm{C}_{4} \times \mathrm{A}_4$4816··2
$((\mathrm{C}_4 \times \mathrm{C}_2) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$4830··1
$\mathrm{C}_{12} \times \mathrm{C}_{4}$4848··5
$\mathrm{G}(4,4,3) \times \mathrm{C}_3$4830··1
$\mathrm{C}_{12} \times \mathrm{C}_{2} \times \mathrm{C}_{2}$4848··4
$\mathrm{S}_3 \times \mathrm{C}_3 \times \mathrm{C}_3$5427··2
$\mathrm{C}_{6} \times \mathrm{C}_{3} \times \mathrm{C}_{3}$5454··3
$\mathrm{C}_{30} \times \mathrm{C}_{2}$6060··1
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$7272··5
$\mathrm{C}_{12} \times \mathrm{C}_{6}$7272··6
$((\mathrm{C}_2 \times \mathrm{C}_6) \rtimes \mathrm{C}_2) \times \mathrm{C}_3$7227··16
$\mathrm{G}(3,8,2) \times \mathrm{C}_3$7236··2
$\mathrm{S}_3 \times \mathrm{C}_{12}$7236··6
$\mathrm{C}_{12} \times \mathrm{C}_{4} \times \mathrm{C}_{2}$9696··1
$\mathrm{G}(3,4,2) \times \mathrm{C}_3 \times \mathrm{C}_3$10854··2
$\mathrm{S}_3 \times \mathrm{C}_6 \times \mathrm{C}_3$10854··4
$\mathrm{C}_{6} \times \mathrm{C}_{6} \times \mathrm{C}_{3}$108108··3
$\mathrm{C}_{12} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$144144··1