C₁₁×#12423 #14589616

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12423

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

218 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 82 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)(13,16)(14,18)(17,19)(20,21,23,26)(22,30,31,48)(24,36,34,49)(25,39,35,29)(27,43,41,32)(28,45,42,38)(33,50,40,46)(37,47,51,44);(12,13,14,16,15,17,18,19)(21,26)(27,41)(28,42)(29,39)(30,48)(36,49)(44,47)(46,50);(20,22,23,31)(21,27,26,41)(24,37,34,51)(25,40,35,33)(28,46,42,50)(29,47,39,44)(30,49,48,36)(32,45,43,38)

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5411);