C₁₁×#12359 #14589552

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12359

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×D₈	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×Q₈×C₁₁ ◁ G

296 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 86 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)(13,17)(14,18)(15,19)(20,21,26,30)(22,31,34,50)(23,28,25,40)(24,36,39,48)(27,42,45,33)(29,35,47,38)(32,49,41,46)(37,43,51,44);(12,13,16,14)(15,18,19,17)(20,22,26,34)(21,27,30,45)(23,32,25,41)(24,37,39,51)(28,43,40,44)(29,46,47,49)(31,48,50,36)(33,35,42,38);(12,14,16,13)(15,17,19,18)(20,23,26,25)(21,28,30,40)(22,32,34,41)(24,35,39,38)(27,43,45,44)(29,36,47,48)(31,49,50,46)(33,37,42,51)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5347);