C₁₁×#12080 #14589273

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12080

Subgroups

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

218 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 90 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)(12,13,15,14,16,17,19,18)(21,25,27,33)(22,29)(23,30)(26,32,34,28)(31,35);(20,21,24,27)(22,26,31,34)(23,32,30,28)(25,29,33,35);(12,14,15,17,16,18,19,13)(20,22,30,35,24,31,23,29)(21,26,28,25,27,34,32,33)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5068);