C₁₁×#9446 #14586639

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9443
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₁×#9446

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂×C₁₁×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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)(14,20)(15,23,25,18)(16,22)(17,19)(21,24,27,26)(28,29)(30,33,37,40)(31,34)(32,35)(36,39,42,43)(38,41);(12,14,20,13,17,22,16,19)(15,21,24,18,25,27,26,23)(28,30,32,37)(29,33)(31,36,38,42)(34,39)(35,40)(41,43);(12,15,17,25)(13,18,19,23)(14,21,22,27)(16,26,20,24)(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,39,40,43)

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, 2434);