C₁₁×#12509 #14589702

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₁×#12509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#1712	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

306 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 110 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)(29,36)(30,41)(31,32)(33,34)(37,42)(38,40)(39,43);(12,14,15,21,16,22,24,27)(13,17,19,20,18,25,23,26)(28,29,37,43,33,39,31,36,35,41,32,38,34,40,42,30);(13,18)(17,25)(19,23)(20,26)(28,30,42,40,34,38,32,41,35,36,31,39,33,43,37,29)

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5497);