Finite Group Databasebeta

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C5×#63385 #13083828

order1440
isoclinismisoclinic class of #63385
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#63385

Splittings

FittingC5×C9×D8 ⋊ C2
HallC5×C9 ⋊ D16
SylowC9 ⋊ C5×D16

Subgroups

subgroupG/H
centerC2×C5#3673
commutator, cosocleC8×C9C22×C5
FrattiniC3×C8C2×C5×D3
FittingC5×C9×D8C2
socleC2×C3×C5#213
hypercenterC5×D8D9
hypocenterC9C5×D16
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×D8

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5)(6,14,9,12,11,10,8,7,13)(16,20)(17,24)(18,25)(21,22)(23,29)(26,30)(27,28);(7,9)(8,12)(10,11)(13,14)(15,16)(17,20)(18,27)(19,23)(21,24)(22,25)(26,29)(28,30)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 145);