C₁₁×#19096 #14596289

order	2816
nilpotency class	3
isoclinism	isoclinic class of #19086
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#19096

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

906 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 906 conjugacy classes of subgroups — too many to draw. Only its 218 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) = 704

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

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

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 12084);