C₁₁×#11490 #14588683

order	2816
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11490

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₁₁×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 1408

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

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4478);