C₁₁×#11729 #14588922

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11692
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₁×#11729

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₁₁×#2635	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×D₄×C₁₁ ◁ G

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

normal subgroups only

This group has 486 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) = 352

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

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

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, 4717);