C₂×C₃³×C₂₃ #11927877

order	1242
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 247104
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₂×C₃³×C₂₃

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1242

A minimal faithful permutation representation — 3 generators on 34 points:

(1,2)(3,4,5)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34);(6,7,8);(9,10,11)

1242 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1242, 30);