C₁₁×#11994 #14589187

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11994
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11994

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1558
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×M₁₆ ◁ G

258 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 98 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)(12,13,15,20,29,21,39,38,17,22,28,37,16,19,30,35)(14,23,25,36,31,34,27,42,24,40,41,43,26,18,32,33);(12,14,17,24)(13,18)(15,27,28,32)(16,31,29,26)(19,23)(20,36)(21,40)(22,34)(25,30,41,39)(33,38)(35,42)(37,43);(15,28)(20,37)(25,41)(27,32)(30,39)(33,42)(35,38)(36,43)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4982);