C₁₁×#32899 #14610092

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₁₁×#32899

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

3866 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3866 conjugacy classes of subgroups — too many to draw. Only its 366 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) = 31
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

539 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 25887);