C₁₁×#9001 #14586194

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#9001

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂×C₁₁×#496	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

662 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 1408

A minimal faithful permutation representation — 3 generators on 31 points:

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

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, 1989);