C₁₁×#7468 #14584661

order	2816
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7468

Subgroups

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

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

normal subgroups only

This group has 182 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) = 47
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 2 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11)(16,17,18,23,19,24,27,35,20,25,28,36,29,37,40,45,21,22,26,32,30,33,38,42,31,34,39,43,41,44,46,47);(12,13,14,15)(17,22)(18,26)(24,33)(25,34)(27,38)(28,39)(37,44)(40,46)

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, 456);