C₁₁×#23899 #14601092

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23897
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₁×#23899

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 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 — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,19)(16,28)(17,21)(18,25)(20,31)(23,39)(24,36)(26,37)(27,35)(29,32)(30,34)(33,41)(38,40)(42,43);(18,32)(22,36)(33,43)(38,39);(12,14)(13,18)(15,23)(16,29)(17,24)(19,33)(20,36)(21,32)(22,28)(25,31)(26,42)(27,40)(30,41)(34,38)(35,43)(37,39);(12,15,17,27)(13,19,21,35)(14,23,24,40)(16,30,31,26)(18,33,32,43)(20,37,28,34)(22,38,36,39)(25,42,29,41)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16887);