C₁₁×#32705 #14609898

order	2816
nilpotency class	3
isoclinism	isoclinic class of #31077
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#32705

Subgroups

	subgroup	G/H
center	C₄×C₁₁	H(3,𝔽₄)
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂×C₁₁	#2804
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

536 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 194 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)(12,13,17,21,18,23,16,22)(14,24,27,19,28,35,26,36)(15,29,33,20,31,39,32,38)(25,40,41,37,42,34,30,43);(12,14)(13,19)(15,30)(16,26)(17,27)(18,28)(20,37)(21,35)(22,24)(23,36)(25,33)(29,40)(31,41)(32,42)(34,39)(38,43);(12,15,18,31)(13,20)(14,25)(16,32,17,33)(19,34,36,40)(21,39)(22,29)(23,38)(24,37,35,43)(26,30)(27,41)(28,42);(14,26,28,27)(15,31)(19,35,36,24)(20,38)(25,41,42,30)(29,39)(32,33)(34,37,40,43)

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, 25693);