C₁₁×#11916 #14589109

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11916

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1533
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	#97	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

274 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 90 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)(12,13,15,21,16,22,29,40,17,19,28,36,31,20,37,38)(14,23,24,41,25,18,32,34,26,35,42,39,30,33,27,43);(12,14,17,26)(13,18,19,33)(15,27,28,32)(16,30,31,25)(20,35,22,23)(21,39,36,41)(24,29,42,37)(34,38,43,40);(13,19)(15,28)(18,33)(20,22)(23,35)(24,42)(27,32)(29,37)

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, 4904);