Finite Group Databasebeta

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C3×#66138 #11755815

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#66138

Splittings

FittingC22×C3×C5×D4 ⋊ C2
HallC3×C5 ⋊ #534
SylowC5 ⋊ C3×#534

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC22×C3×C5×D4C2
socleC22×C3×C5C24
hypercenterC22×C3×D4D5
hypocenterC5C3×#534
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×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)(4,5,7,8,6)(10,12)(15,19)(17,20);(14,18)(17,20);(13,15)(14,17)(16,19)(18,20);(5,6)(7,8)(9,10)(11,12)(13,14)(15,17)(16,18)(19,20)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10600827, C3×#10600817, C3×#10602449, …
maximal normal subgroup ofC3×#10600827, C3×#10600817, C3×#10602449, …
maximal quotient ofC3×#10613852, C3×#10615774, C3×#10613826, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10010);