hyperelliptic(.ncag).info

the group $\mathrm{C}_{12} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$

GAP SmallGroup id

$[144, 178]$

order

$144$

structure

$\mathrm{C}_{12} \times \mathrm{C}_{6} \times \mathrm{C}_{2}$

presentation

$\langle g_{1}, g_{2}, g_{3}, g_{4}, g_{5}, g_{6} \mid g_{1}^{2}g_{6}^{-1},\; g_{2}^{-1}g_{1}^{-1}g_{2}g_{1},\; g_{3}^{-1}g_{1}^{-1}g_{3}g_{1},\; g_{4}^{-1}g_{1}^{-1}g_{4}g_{1},\; g_{5}^{-1}g_{1}^{-1}g_{5}g_{1},\; g_{6}^{-1}g_{1}^{-1}g_{6}g_{1},\; g_{2}^{2},\; g_{3}^{-1}g_{2}^{-1}g_{3}g_{2},\; g_{4}^{-1}g_{2}^{-1}g_{4}g_{2},\; g_{5}^{-1}g_{2}^{-1}g_{5}g_{2},\; g_{6}^{-1}g_{2}^{-1}g_{6}g_{2},\; g_{3}^{2},\; g_{4}^{-1}g_{3}^{-1}g_{4}g_{3},\; g_{5}^{-1}g_{3}^{-1}g_{5}g_{3},\; g_{6}^{-1}g_{3}^{-1}g_{6}g_{3},\; g_{4}^{3},\; g_{5}^{-1}g_{4}^{-1}g_{5}g_{4},\; g_{6}^{-1}g_{4}^{-1}g_{6}g_{4},\; g_{5}^{3},\; g_{6}^{-1}g_{5}^{-1}g_{6}g_{5},\; g_{6}^{2} \rangle$

character table

Columns are the conjugacy classes: order is the order of a class representative, size the number of elements in the class. Rows $\chi_i$ are the irreducible characters.