C₁₁×#13834 #14591027

order	2816
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₁ · Schur multiplier (H₂) = C₂×C₄³

Aliases

direct product

C₁₁×#13834

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

1390 conjugacy classes of subgroups; only the 622 normal subgroups are shown.

normal subgroups only

This group has 1390 conjugacy classes of subgroups — too many to draw. Only its 622 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) = 2816

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6822);