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C5×#5804 #11756189

order960
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#5804

Splittings

FittingC22×C3×C5×D4 ⋊ C2
HallC3×C5 ⋊ #534
SylowC3 ⋊ C5×#534

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC22×C3×C5×D4C2
socleC22×C3×C5C24
hypercenterC22×C5×D4D3
hypocenterC3C5×#534
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C5×D4

692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#70034, C5×#70024, C5×#71656, …
maximal normal subgroup ofC5×#70034, C5×#70024, C5×#71656, …
maximal quotient ofC5×#82121, C5×#84043, C5×#82095, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10384);