C₁₁×#12062 #14589255

order	2816
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12062

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₄	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₈×D₄
prime radical	C₂×C₁₁×D₈	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₄×C₁₁×C₁₆ ◁ G

252 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 130 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)(12,13,15,17)(14,16,19,18)(20,21,23,27,24,28,31,34,25,22,26,29,32,30,33,35);(13,16)(14,19)(17,18);(13,17)(16,18)(20,22,23,29,24,30,31,35,25,21,26,27,32,28,33,34)

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5050);