C₁₁×#10641 #14587834

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10637
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10641

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

330 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 102 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)(12,13,16,17,15,19,14,18)(20,21,25,26,24,29,23,28)(22,30,32,27,31,34,33,35);(21,26)(22,31)(23,25)(27,30)(28,29)(34,35);(13,17)(14,16)(18,19)(20,22,23,32,24,31,25,33)(21,27,28,34,29,35,26,30)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3629);