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C11×#24223 #14601416

order2816
nilpotency class3
isoclinismisoclinic class of #23906
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C26

Aliases

direct productC11×#24223

Subgroups

subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 704

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

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

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, 17211);