C₁₁×#12363 #14589556

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12363

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₁₁×#446 ◁ G

278 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 82 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)(13,17)(14,18)(15,19)(20,21,25,29)(22,30,32,49)(23,34,36,48)(24,39,37,28)(26,41,42,31)(27,44,46,38)(33,50,40,45)(35,47,51,43);(12,13,16,14)(15,18,19,17)(20,22,25,32)(21,26,29,42)(23,35,36,51)(24,40,37,33)(27,45,46,50)(28,47,39,43)(30,48,49,34)(31,44,41,38);(12,14,16,13)(15,17,19,18)(23,36)(27,46)(30,49)(31,41)(34,48)(35,51)(38,44)(45,50)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5351);