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C11×#24398 #14601591

order2816
nilpotency class3
isoclinismisoclinic class of #24398
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C26

Aliases

direct productC11×#24398

Subgroups

subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

1476 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)(12,13)(14,15)(16,17,20,24,19,23,29,22)(18,25,26,31,27,21,28,30);(13,15)(16,18)(17,21)(19,27)(20,26)(22,31)(23,25)(24,30)(28,29);(17,22)(18,26)(20,29)(23,24)(27,28)(30,31);(13,15)(17,23)(21,25)(22,24)(30,31)

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, 17386);