C₁₁×#23840 #14601033

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23391
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#23840

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄³×C₁₁ ◁ G

662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 2816

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16828);