C₁₁×#8810 #14586003

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#8810

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₄³×C₁₁ ◁ G

402 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 39
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1798);