C₁₁×#12312 #14589505

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12310
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12312

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#3292	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

372 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 78 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)(12,13,17,21)(14,22,25,41)(15,27,31,43)(16,32,30,20)(18,33,35,24)(19,37,39,28)(23,38,26,40)(29,34,42,36);(15,28)(16,30)(19,27)(20,32)(22,38)(23,26)(24,29)(31,37)(33,42)(34,36)(39,43)(40,41);(12,14)(13,18)(15,29)(16,23)(17,25)(19,38)(20,34)(21,35)(22,27)(24,28)(26,30)(31,42)(32,36)(33,37)(39,40)(41,43)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5300);