C₁₁×#13331 #14590524

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13331

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

650 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 122 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 — 3 generators on 31 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6319);