C₁₁×#12047 #14589240

order	2816
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12047

Subgroups

	subgroup	G/H
center	C₈×C₁₁	C₂×D₈
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂×C₁₁	C₈×D₈
prime radical	C₁₁×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ C₄×C₁₁×C₁₆ ◁ G

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5035);