C₁₁×#13340 #14590533

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13340
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13340

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#493
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#2011
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

552 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 118 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)(14,25)(15,22)(16,21)(17,35)(18,23)(19,26)(20,27)(24,31)(28,37)(29,43)(30,40)(32,42)(33,38)(34,41)(36,39);(12,14)(13,19)(15,30)(16,26)(17,36)(18,29)(20,35)(21,39)(22,25)(23,38)(24,40)(27,32)(28,31)(33,34)(37,41)(42,43);(12,14)(13,20)(15,27)(16,33)(17,36)(18,29)(19,24)(21,25)(22,37)(23,40)(26,34)(28,31)(30,32)(35,38)(39,42)(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, 6328);