C₁₁×#11500 #14588693

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11499
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11500

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁴×C₁₁ ◁ C₂²×C₁₁×C₂²⋊C₄ ◁ G

706 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 118 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)(12,13,14,17,15,16,18,19)(20,21)(22,28)(23,31,32,26)(24,27)(25,29,33,35)(30,34);(20,22,24,30)(21,25,27,33)(23,29,32,35)(26,28,31,34);(13,16)(17,19)

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, 4488);