C₁₁×#12502 #14589695

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12502

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 59
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,22,27)(15,24,21,18)(17,25,26,23)(28,29)(30,38)(31,34)(32,44)(33,47)(35,40)(36,46)(37,43)(39,54)(41,58)(42,55)(45,53)(48,52)(49,56)(50,57)(51,59);(12,14,21,25,16,22,15,23)(13,17,24,27,19,26,18,20)(29,34)(35,49)(36,50)(37,47)(38,54)(44,55)(51,53)(52,58);(14,22)(17,26)(20,27)(23,25)(28,30,31,39)(29,35,34,49)(32,45,42,59)(33,48,43,41)(36,52,50,58)(37,53,47,51)(38,55,54,44)(40,57,56,46)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5490);