Finite Group Databasebeta

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C3×#66063 #11755740

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

Aliases

direct productC3×#66063

Splittings

FittingC3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ #544
SylowC5 ⋊ C3×#544

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×C4⋊Q8C2
socleC22×C3×C5C24
prime radicalC22×C3×D5C23
hypercenterC3×C4⋊Q8D5
hypocenterC5C3×#544
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

412 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)(10,14,15,16)(17,19,20,24)(18,21,22,23);(11,12)(14,16)(17,18,20,22)(19,23,24,21);(9,11,13,12)(10,14,15,16);(5,6)(7,8)(9,10)(11,14)(12,16)(13,15)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10612698, C3×#10612793, #14430792, …
maximal normal subgroup ofC3×#10612698, C3×#10612793, #14430792, …
maximal quotient ofC3×#10607926, C3×#10606090, C3×#10607699, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9935);