Finite Group Databasebeta

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C11×#24416 #14601609

order2816
nilpotency class3
isoclinismisoclinic class of #24412
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C26

Aliases

direct productC11×#24416

Subgroups

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

1448 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)(16,17,20,22,19,23,26,27)(18,21,25,29,24,30,28,31);(12,13)(14,15)(20,26)(22,27)(25,28)(29,31);(13,15)(16,17)(18,21)(19,23)(20,27)(22,26)(24,30)(25,31)(28,29);(16,18,19,24)(17,21,23,30)(20,28,26,25)(22,31,27,29)

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 17404);