C₁₁×#32873 #14610066

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32873
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₁×#32873

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2840
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂³×D₄×C₁₁	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂⁴×C₁₁ ◁ G

854 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 186 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) = 27
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 4 generators on 27 points:

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

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 25861);