C₁₁×#13077 #14590270

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13077

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

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

normal subgroups only

This group has 470 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)(14,24,27,39)(15,20,30,38)(16,31)(17,23)(18,36)(19,26,37,32)(21,25)(22,35)(28,29,42,33)(34,43)(40,41);(12,14,25,38,35,42,16,32,17,27,41,20,18,28,34,26)(13,19,31,29,36,15,21,39,23,37,43,33,22,30,40,24);(12,15)(13,20)(14,21)(16,33)(17,30)(18,19)(22,32)(23,38)(24,41)(25,39)(26,36)(27,40)(28,31)(29,34)(35,37)(42,43)

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, 6065);