C₁₁×#7088 #14584281

order	2816
nilpotency class	4
isoclinism	isoclinic class of #7076
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7088

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#327
commutator	C₂²×C₈	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₄⋊C₈	C₂²×C₁₁
prime radical	C₂²×C₁₁×D₈	C₄
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

248 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 54 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)(12,13,14,17,15,16,18,19)(20,21)(22,25)(23,32)(24,28)(26,29)(27,30)(31,34)(33,35);(13,16)(21,25)(22,29)(23,30)(26,27)(28,34)(31,35)(32,33)

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, 76);