C₁₁×#12449 #14589642

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12449

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×D₈	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

222 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 82 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)(12,13,16,19)(14,20,23,27)(15,24,21,18)(17,25,26,22)(28,29)(30,33)(31,34)(32,40)(35,39)(36,38)(37,41)(42,43);(12,14,21,25,16,23,15,22)(13,17,24,27,19,26,18,20)(29,33)(34,41)(35,42)(36,40);(29,34)(31,39)(32,38)(33,41)(35,36)(37,43)(40,42)

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5437);