C₂×C₃³×C₃₁ #13131966

order	1674
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 336960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₂×C₃³×C₃₁

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1674

A minimal faithful permutation representation — 3 generators on 42 points:

(1,2)(3,4,5)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42);(6,7,8);(9,10,11)

1674 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1674, 60);