Finite Group Databasebeta

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C3×#65847 #11755524

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

Aliases

direct productC3×#65847

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ #552
SylowC5 ⋊ C3×#552

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC2×C3×C5×C4⋊C4C2
socleC22×C3×C5C24
prime radicalC2×C3×C22⋊D5C22
hypercenterC2×C3×C4⋊C4D5
hypocenterC5C3×#552
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4⋊C4

428 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)(18,22)(21,24);(10,14)(11,15)(17,19,20,23)(18,21,22,24);(9,11,12,15)(10,13,14,16);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,21)(20,22)(23,24)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10610490, C3×#10613176, #14458697, …
maximal normal subgroup ofC3×#10610490, C3×#10613176, #14458697, …
maximal quotient ofC3×#10605066, C3×#10613890, C3×#10605364, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9719);