C₁₁×#8188 #14585381

order	2816
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#8188

Subgroups

	subgroup	G/H
center	C₄²×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	C₄×C₂²⋊C₄
prime radical	C₂×C₁₁×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

412 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 1408

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

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

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, 1176);