C₁₁×#12512 #14589705

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12506
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₁×#12512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

268 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,20)(15,23)(16,18)(17,21)(19,24)(22,26)(25,27)(28,29)(30,38)(31,41)(32,40)(33,42)(34,39)(35,37)(36,43);(12,14,15,21,16,22,24,27)(13,17,19,20,18,25,23,26)(28,30,38,29,34,40,33,36,35,31,41,37,43,42,32,39);(13,18)(17,25)(19,23)(20,26)(28,31,41,29,34,42,32,36,35,30,38,37,43,40,33,39)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5500);