C₁₁×#32877 #14610070

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32875
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#32877

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

594 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 186 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)(14,23)(15,27)(16,21)(17,32)(18,22)(19,26)(20,30)(24,39)(25,36)(28,37)(29,43)(31,38)(33,35)(34,41)(40,42);(12,14,17,33,18,26,16,25)(13,19,21,35,22,23,32,36)(15,28,31,24,30,40,29,41)(20,37,38,34,27,42,43,39);(12,15,17,31,18,30,16,29)(13,20,21,38,22,27,32,43)(14,24,25,28,26,41,33,40)(19,34,36,37,23,39,35,42);(12,16,18,17)(13,21,22,32)(14,25,26,33)(15,29,30,31)(19,35,23,36)(20,38,27,43)(24,40,41,28)(34,37,39,42)

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, 25865);