C₁₁×#13304 #14590497

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#13304

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

670 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 138 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)(14,15)(20,21)(22,25)(23,32)(24,28)(26,29)(27,30)(31,34)(33,35);(16,17)(18,19)(21,25)(22,29)(23,30)(26,27)(28,34)(31,35)(32,33);(13,15)(17,19)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6292);