C₁₁×#10038 #14587231

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10038
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10038

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

532 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 43 points:

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

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, 3026);