C₁₁×#13079 #14590272

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×#13079

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

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

normal subgroups only

This group has 486 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)(12,13,18,21,17,23,34,22)(14,24,20,33,27,38,26,16)(15,19,30,36,29,37,31,40)(25,42,35,28,43,41,39,32);(12,14,16,13,18,26,24,22,17,27,33,23,34,20,38,21)(15,25,32,19,31,35,41,36,29,43,28,37,30,39,42,40);(12,15)(13,19)(14,25)(16,32)(17,29)(18,31)(20,39)(21,40)(22,36)(23,37)(24,41)(26,35)(27,43)(28,33)(30,34)(38,42)

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, 6067);