C₂²×C₈²×C₁₃ #15703649

order	3328
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 28311552
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₈

Aliases

C₂²×C₈²×C₁₃

1342 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8)(21,22,23,24,25,26,27,28,29,30,31,32,33);(9,10,11,12,13,14,15,16);(17,18);(19,20)

3328 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 10298);