C₁₁×#10014 #14587207

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10014

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#392
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

566 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 122 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 — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,18)(15,19)(20,21)(22,29)(23,27)(24,32)(25,28)(26,30)(31,35)(33,34);(12,13,16,14)(15,18,19,17)(20,22,25,31)(21,26,28,34)(23,30,24,33)(27,35,32,29);(12,14,16,13)(15,17,19,18)(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,29,34,35)

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, 3002);