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C5×#66851 #13182174

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

Aliases

direct productC5×#66851

Splittings

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
Fitting, prime radicalC32×C5×C13C3
socleC3×C5×C13C32
hypercenterC32×C5C13⋊C3
hypocenterC13C5×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C3×C5 ◁ C32×C5

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

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, 7);