C₁₁×#12163 #14589356

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12102
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12163

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#466	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

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

normal subgroups only

This group has 360 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) = 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)(16,19)(20,21,25,29)(22,30,32,48)(23,34,36,50)(24,39,37,28)(26,41,42,31)(27,44,46,38)(33,49,40,45)(35,47,51,43);(12,13)(14,16)(15,17)(18,19)(20,22)(21,26)(23,35)(24,40)(25,32)(27,45)(28,47)(29,42)(30,34)(31,38)(33,37)(36,51)(39,43)(41,44)(46,49)(48,50);(12,14,15,18)(13,16,17,19)(23,36)(27,46)(30,48)(31,41)(34,50)(35,51)(38,44)(45,49)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5151);