C₂×C₄²×C₈×C₁₉ #18026284

order	4864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 113246208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

C₂×C₄²×C₈×C₁₉

2046 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 4 generators on 37 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 13313);