C₁₁×#13076 #14590269

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13076

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#3060	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

466 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6064);