C₁₁×#12076 #14589269

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12076

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂²×C₁₁	C₄×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ C₈²×C₁₁ ◁ G

210 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 98 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)(22,30,31,49)(23,34,37,48)(25,39,36,29)(26,41,42,32)(27,44,46,38)(33,50,40,45)(35,47,51,43);(20,22,24,31)(21,26,28,42)(23,35,37,51)(25,40,36,33)(27,45,46,50)(29,47,39,43)(30,48,49,34)(32,44,41,38);(12,14,15,17,16,18,19,13)(22,31)(26,42)(30,49)(32,41)(33,40)(35,51)(43,47)(45,50)

Conjugacy classes & character table

638 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5064);