Finite Group Databasebeta

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C3×#66166 #11755843

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

Aliases

direct productC3×#66166

Splittings

FittingC2×C3×C5×#41 ⋊ C2
HallC3×C5 ⋊ #532
SylowC5 ⋊ C3×#532

Subgroups

subgroupG/H
centerC2×C3×C4C22×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC2×C3×C5×#41C2
socleC22×C3×C5C24
hypercenterC2×C3×#41D5
hypocenterC5C3×#532
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#41

620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10604993, #14283983, C3×#10604994, …
maximal normal subgroup ofC3×#10604993, #14283983, C3×#10604994, …
maximal quotient ofC3×#10613955, C3×#10613956, C3×#10613959, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10038);