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C3×#65886 #11755563

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

Aliases

direct productC3×#65886

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #548
SylowC5 ⋊ C3×#548

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
hypercenterC3×C4×D4D5
hypocenterC5C3×#548
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

580 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)(14,18)(17,20);(10,12)(13,15,16,19)(14,17,18,20);(9,10)(11,12);(5,6)(7,8)(10,12)(13,14)(15,17)(16,18)(19,20)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10615222, C3×#10611225, #14453516, …
maximal normal subgroup ofC3×#10615222, C3×#10611225, #14453516, …
maximal quotient ofC3×C22⋊C4×Dic10, C3×#10605185, C3×#10605368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9758);