C₁₁×#9449 #14586642

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9443
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9449

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

490 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 122 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)(12,13,16,20,17,19,15,25)(14,21,24,26,23,27,22,18)(28,29)(30,37,38,41)(31,34,39,40)(32,35)(33,36)(42,43);(12,14,17,23)(13,18)(15,22,16,24)(19,26)(20,21)(25,27)(28,30,32,40,33,38,42,34)(29,31,35,41,36,39,43,37);(13,19)(15,16)(18,26)(22,24)(28,31)(29,34)(30,35)(32,41)(33,39)(36,40)(37,42)(38,43)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2437);