C₁₁×#12095 #14589288

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12093
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12095

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₁₁×#534	C₂²
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₄ ◁ G

458 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 74 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)(14,16)(15,18)(17,19)(20,21)(22,30)(23,27)(24,28)(25,29)(26,32)(31,47)(33,46)(34,45)(35,41)(36,42)(37,44)(38,48)(39,49)(40,50)(43,51);(13,16)(14,19)(17,18)(20,22,25,33)(21,26,29,39)(23,34,36,31)(24,32,37,49)(27,40,42,38)(28,30,44,46)(35,50,51,48)(41,45,43,47);(20,23,25,36)(21,27,29,42)(22,31,33,34)(24,35,37,51)(26,38,39,40)(28,43,44,41)(30,45,46,47)(32,48,49,50)

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5083);