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C11×#23909 #14601102

order2816
nilpotency class3
isoclinismisoclinic class of #23906
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC11×#23909

Subgroups

subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

1802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 352

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

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16897);