C₇²×C₃₂ #13096009

order	1568
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 32256
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₇²×C₃₂

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1568

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39);(40,41,42,43,44,45,46)

1568 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1568, 175);