C₄⁴×C₁₉ #18019703

order	4864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 23781703680
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄⁶

Aliases

C₄⁴×C₁₉

3966 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3,4)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(5,6,7,8);(9,10,11,12);(13,14,15,16)

4864 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6732);