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C5×#64602 #13095628

order1560
isoclinismisoclinic class of #64602
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#64602

Splittings

HallC3×C5×C13 ⋊ D4
HallC5×C13 ⋊ #67
HallC3×C13 ⋊ C5×D4
HallC3×C5 ⋊ C22⋊D13
SylowC13 ⋊ C5×#67
SylowC3 ⋊ C5×C22⋊D13

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×D13
commutator, cosocleC2×C3×C13C22×C5
FrattiniC2C5×D3×D13
Fitting, socleC2×C3×C5×C13C22
hypocenterC3×C13C5×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 780

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 64);