C₁₁×#13611 #14590804

order	2816
nilpotency class	5
isoclinism	isoclinic class of #13609
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13611

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2127
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₁
prime radical	C₁₁×#3221	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#536 ◁ G

316 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 86 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)(12,13,15,21,17,22,28,36)(14,19,24,32,23,33,37,43)(16,18,26,31,29,20,27,35)(25,30,40,41,38,34,39,42);(13,18)(14,23)(15,26)(16,29)(19,30)(20,22)(24,39)(27,28)(31,35)(33,34)(37,40)(41,42);(12,14)(13,19)(15,24)(16,25)(17,23)(18,30)(20,34)(21,32)(22,33)(26,40)(27,39)(28,37)(29,38)(31,41)(35,42)(36,43)

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6599);