C₁₁×#12065 #14589258

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12065

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#442
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×D₈	C₂×C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₁₁×#322 ◁ G

230 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 35
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 35 points:

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

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, 5053);