C₁₁×#12405 #14589598

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12405

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×Q₈×C₁₁ ◁ G

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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 — 3 generators on 43 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5393);