Finite Group Databasebeta

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C3×#65902 #11755579

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

Aliases

direct productC3×#65902

Splittings

FittingC3×C4×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #556
SylowC5 ⋊ C3×#556

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×Q8C2
socleC22×C3×C5C24
prime radicalC2×C3×D20C22
hypercenterC3×C4×Q8D5
hypocenterC5C3×#556
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3)(4,5,7,8,6)(9,12,13,11)(10,15,16,14)(18,22)(21,24);(9,11,13,12)(10,15,16,14)(17,19,20,23)(18,21,22,24);(9,11,13,12)(10,14,16,15)(17,18)(19,21)(20,22)(23,24);(5,6)(7,8)(9,10,13,16)(11,14,12,15)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10611351, C3×#10612946, #14471627, …
maximal normal subgroup ofC3×#10611351, C3×#10612946, #14471627, …
maximal quotient ofC3×#10605366, C3×#10605370, C3×#10605373, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9774);