C₂×C₁₁×#2868 #14613836

order	2816
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

direct product

C₂×C₁₁×#2868

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

3774 conjugacy classes of subgroups; only the 1886 normal subgroups are shown.

normal subgroups only

This group has 3774 conjugacy classes of subgroups — too many to draw. Only its 1886 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) = 29
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 5 generators on 29 points:

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

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, 29631);