C₁₁×#12290 #14589483

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12102
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12290

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#466	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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)(12,13,16,19)(14,17,21,24)(15,18,22,25)(20,26,27,23)(29,34)(30,33)(31,38)(35,43)(36,42)(37,40)(39,41);(12,14)(13,17)(15,20)(16,21)(18,23)(19,24)(22,27)(25,26)(28,29)(30,35)(31,39)(32,36)(33,41)(34,38)(37,42)(40,43);(12,15,16,22)(13,18,19,25)(14,20,21,27)(17,23,24,26)(28,30,32,33)(29,35,36,41)(31,37,40,38)(34,39,42,43)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5278);