C₁₁×#12304 #14589497

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12304

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₁₁×#3259	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

286 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 70 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)(12,13,18,22,17,23,16,33)(14,24,34,41,26,20,27,37)(15,28,29,38,31,19,32,21)(25,35,42,36,30,39,43,40);(13,19)(15,29)(16,18)(20,35)(21,33)(22,38)(23,28)(24,39)(25,42)(27,34)(30,43)(31,32)(36,41)(37,40);(12,14,17,26)(13,20)(15,30,31,25)(16,27,18,34)(19,35)(21,36)(22,37)(23,24)(28,39)(29,43,32,42)(33,41)(38,40)

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5292);