C₁₁×#32901 #14610094

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₁₁×#32901

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#585	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

3706 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3706 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) = 704

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)(16,17,21,20)(18,22,26,25)(19,23,28,27)(24,30,31,29);(16,18)(17,22)(19,24)(20,25)(21,26)(23,29)(27,30)(28,31);(16,19)(17,23)(18,24)(20,27)(21,28)(22,29)(25,30)(26,31);(13,15)(16,20,21,17)(18,25,26,22)(19,27,28,23)(24,30,31,29)

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, 25889);