C₁₁×#8801 #14585994

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#8801

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#117
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#383
prime radical	C₂³×C₁₁	#117
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

306 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 704

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

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1789);