C₁₁×#23896 #14601089

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₁×#23896

Subgroups

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

1764 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1764 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)(14,18)(15,19)(16,20)(17,21)(22,28)(23,29)(24,30)(25,38)(26,33)(27,34)(31,36)(32,39)(35,42)(37,41)(40,43);(12,14,17,24)(13,18,21,30)(15,22,26,36)(16,23,27,37)(19,31,33,28)(20,29,34,41)(25,35,39,43)(32,42,38,40);(12,15)(13,19)(14,22)(16,25)(17,26)(18,28)(20,32)(21,33)(23,35)(24,36)(27,39)(29,40)(30,31)(34,38)(37,43)(41,42);(12,16)(13,20)(14,23)(15,25)(17,27)(18,29)(19,32)(21,34)(22,35)(24,37)(26,39)(28,40)(30,41)(31,42)(33,38)(36,43)

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, 16884);