C₁₁×#12075 #14589268

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12075

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₄×D₈
prime radical	C₂×C₁₁×D₈	C₂×C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ C₈²×C₁₁ ◁ G

224 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 98 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)(12,13,15,14,16,17,19,18)(21,25)(22,28)(23,30)(26,34)(27,35)(29,32)(31,33);(20,21,24,26)(22,29,31,35)(23,32,30,27)(25,33,34,28);(12,14,15,17,16,18,19,13)(21,26)(25,34)(27,32)(29,35)

Conjugacy classes & character table

638 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5063);