Finite Group Databasebeta

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C3×#65961 #11755638

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

Aliases

direct productC3×#65961

Splittings

FittingC3×C5×C22⋊Q8 ⋊ C2
HallC3×C5 ⋊ #525
SylowC5 ⋊ C3×#525

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C22⋊Q8C2
socleC22×C3×C5C24
hypercenterC3×C22⋊Q8D5
hypocenterC5C3×#525
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊Q8

660 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)(9,10,11,12)(14,18)(17,20);(10,12)(13,15,16,19)(14,17,18,20);(10,12)(13,14)(15,17)(16,18)(19,20);(5,6)(7,8)(10,12)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10599126, C3×#10604498, #14282831, …
maximal normal subgroup ofC3×#10599126, C3×#10604498, #14282831, …
maximal quotient ofC3×#10605593, C3×#10606108, C3×#10606668, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9833);