C₂⁴×C₈×C₂₉ #16817283

order	3712
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 578027520
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂⁴×C₈×C₂₉

1976 conjugacy classes of subgroups.

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 5 generators on 45 points:

(1,2,3,4,5,6,7,8)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(9,10);(11,12);(13,14);(15,16)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2301);