Finite Group Databasebeta

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C5×#81760 #14438880

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4

Aliases

direct productC5×#81760

Splittings

FittingC3×C5×#492 ⋊ C2
HallC3×C5 ⋊ #3147
SylowC3 ⋊ C5×#3147

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#492C2
socleC22×C3×C5C22×D4
hypercenterC5×#492D3
hypocenterC3C5×#3147
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#492

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 164578);