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C5×#81848 #14439543

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

Aliases

direct productC5×#81848

Splittings

FittingC3×C5×#496 ⋊ C2
HallC3×C5 ⋊ #3155
SylowC3 ⋊ C5×#3155

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×#3155
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#496

1192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

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

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

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, 165241);