C₁₁×#12079 #14589272

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12079

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#442
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₁₁×#322 ◁ G

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

normal subgroups only

This group has 204 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) = 51
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14,16,17,19,18)(20,21,24,28,26,30,25,41)(22,31,33,49,35,50,34,46)(23,36,39,48,38,47,40,29)(27,42,44,32,45,37,43,51);(20,22,26,35)(21,27,30,45)(23,37,38,42)(24,34,25,33)(28,43,41,44)(29,46,48,49)(31,36,50,47)(32,40,51,39);(12,14,15,17,16,18,19,13)(21,28,30,41)(23,38)(27,43,45,44)(29,47,48,36)(31,49,50,46)(32,51)(37,42)(39,40)

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, 5067);