Finite Group Databasebeta

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C5×#66849 #13182171

order1755
isoclinismisoclinic class of #66848
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#66849

Splittings

FittingC5×C9×C13 ⋊ C3
HallC5×C13 ⋊ 3−1+2
SylowC13 ⋊ C5×3−1+2

Subgroups

subgroupG/H
centerC3×C5C3×C13⋊C3
commutator, cosocleC3×C13C32×C5
FrattiniC3C3×C5×C13⋊C3
FittingC5×C9×C13C3
socleC3×C5×C13C32
prime radicalC3×C5×C13⋊C3C3
hypercenterC5×C9C13⋊C3
hypocenterC13C5×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C3×C5 ◁ C5×C9

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 585

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1755, 4);