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C5×#81844 #14439069

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

Aliases

direct productC5×#81844

Splittings

FittingC3×C5×#496 ⋊ C2
HallC3×C5 ⋊ #3150
SylowC3 ⋊ C5×#3150

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#496C2
socleC22×C3×C5C22×D4
hypercenterC5×#496D3
hypocenterC3C5×#3150
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#496

1128 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)(15,24,23,25)(19,22,27,28);(6,7,8)(9,10,11,12)(15,23)(19,27)(22,28)(24,25);(13,15,17,25,18,23,16,24)(14,19,20,22,21,27,26,28);(10,12)(13,14)(15,22)(16,20)(17,26)(18,21)(19,25)(23,28)(24,27)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 164767);