C₁₁×#33564 #14610757

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2202
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₁×#33564

Subgroups

	subgroup	G/H
center	C₄×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₁
socle	C₂×C₁₁	C₂×B(4,𝔽₂)
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#41 ◁ G

1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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) = 352

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 26552);