C₁₁×#13330 #14590523

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13330

Subgroups

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

558 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 146 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)(14,15)(20,21,26,31)(22,32,23,35)(24,38,43,51)(25,44,41,30)(27,36,28,33)(29,47,50,42)(34,49,37,48)(39,46,40,45);(13,15)(16,17)(18,19)(20,22,26,23)(21,27,31,28)(24,39,43,40)(25,37,41,34)(29,48,50,49)(30,46,44,45)(32,51,35,38)(33,47,36,42);(17,19)(20,23,26,22)(21,28,31,27)(24,40,43,39)(25,34,41,37)(29,49,50,48)(30,45,44,46)(32,38,35,51)(33,42,36,47)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6318);