C₁₁×#10512 #14587705

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10512
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#3245	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

408 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 94 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)(12,13)(14,17)(15,18)(16,19)(20,21)(22,29)(23,25)(24,28)(26,30)(27,32)(31,34)(33,35);(12,13)(14,18)(15,17)(16,19)(21,25)(22,30)(23,32)(26,34)(27,28)(29,33);(13,17)(14,15)(18,19)(20,22,23,31,24,30,32,35)(21,26,27,34,28,29,25,33)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3500);