C₂×C₄³×C₂₉ #16815979

order	3712
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 154140672
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

C₂×C₄³×C₂₉

1272 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(5,6,7,8);(9,10,11,12);(13,14)

3712 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 997);