C₁₁×#23795 #14600988

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23414
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#23795

Subgroups

	subgroup	G/H
center	C₄×C₁₁	C₂×#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂×C₁₁	#2397
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

908 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 250 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)(12,13,16,20,17,21,29,35)(14,22,24,30,25,34,28,18)(15,19,27,33,26,32,39,42)(23,36,38,41,37,43,40,31);(12,14)(13,18)(15,23)(16,28)(17,25)(19,31)(20,34)(21,30)(22,35)(24,29)(26,37)(27,40)(32,41)(33,43)(36,42)(38,39);(15,26)(18,30)(19,32)(22,34)(23,37)(27,39)(33,42)(38,40);(12,15,16,27,17,26,29,39)(13,19,20,33,21,32,35,42)(14,23,28,40,25,37,24,38)(18,31,34,43,30,41,22,36)

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, 16783);