C₃²×C₈×C₁₇ #11927465

order	1224
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3072
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₈×C₁₇

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1224

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4,5,6,7,8)(9,10,11)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(12,13,14)

1224 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1224, 38);