C₁₁×#12269 #14589462

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12148
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12269

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₄ ◁ G

372 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(28,29,32,36)(30,37,39,34)(31,40,42,35)(33,41,43,38);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24)(28,30,32,39)(29,33,36,43)(31,41,42,38)(34,40,37,35);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,30)(29,34,36,37)(31,38)(32,39)(33,35,43,40)(41,42)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5257);