C₁₁×#7370 #14584563

order	2816
nilpotency class	5
isoclinism	isoclinic class of #1408
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#7370

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#353
commutator	C₄²	C₂×C₈×C₁₁
Frattini, cosocle	#384	C₂²×C₁₁
prime radical	C₂³×C₁₁	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#384 ◁ G

190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 35 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 358);