Finite Group Databasebeta

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C3×#90783 #13063534

order1392
isoclinismisoclinic class of #90782
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#90783

Splittings

HallC3×C29 ⋊ SD16
SylowC29 ⋊ C3×SD16

Subgroups

subgroupG/H
centerC2×C3C22⋊D29
commutator, cosocleC4×C29C22×C3
FrattiniC4C2×C3×D29
Fitting, prime radicalC3×D4×C29C2
socleC2×C3×C29D4
hypercenterC3×D4D29
hypocenterC29C3×SD16
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 696

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,32,30,28,26,24,22,20,18,16,14,12,10,8,6)(34,37)(35,40)(38,39);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34,36,39)(35,37,40,38)

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 45);