C₁₁×#32948 #14610141

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₁×#32948

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

1334 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 290 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)(13,18)(16,19)(20,28)(21,29)(22,30)(23,36)(24,31)(26,32)(33,42)(34,39)(35,40)(38,43);(12,13,19,30,17,22,16,18)(14,20,31,39,25,34,24,28)(15,21,32,40,27,35,26,29)(23,33,41,42,36,43,37,38);(12,14)(13,20)(15,23)(16,24)(17,25)(18,28)(19,31)(21,33)(22,34)(26,37)(27,36)(29,38)(30,39)(32,41)(35,43)(40,42);(12,15)(13,21)(14,23)(16,26)(17,27)(18,29)(19,32)(20,33)(22,35)(24,37)(25,36)(28,38)(30,40)(31,41)(34,43)(39,42)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 25936);