C₁₁×#62694 #14639887

order	2816
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₁ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₁₁×#62694

Subgroups

	subgroup	G/H
center	C₄²×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
socle	C₂²×C₁₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ G

6640 conjugacy classes of subgroups; only the 5670 normal subgroups are shown.

normal subgroups only

This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 5670 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 — 6 generators on 43 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55682);