C₂×C₈×C₁₆×C₁₉ #18017355

order	4864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 589824
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₈

Aliases

C₂×C₈×C₁₆×C₁₉

398 conjugacy classes of subgroups.

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(17,18,19,20,21,22,23,24);(25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4384);