C₅×C₇²×C₈ #14519949

order	1960
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 32256
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₅×C₇²×C₈

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 2 generators on 27 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)

1960 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 46);