C₁₁×#12884 #14590077

order	2816
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#12884

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

302 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 166 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) = 704

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5872);