Finite Group Databasebeta

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C3×#65889 #11755566

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

Aliases

direct productC3×#65889

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #547
SylowC5 ⋊ C3×#547

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
hypercenterC3×C4×D4D5
hypocenterC5C3×#547
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

584 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)(9,10,11,12);(14,18)(15,19);(13,15,16,19)(14,17,18,20);(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×#10601811, C3×#10598993, #14289118, …
maximal normal subgroup ofC3×#10601811, C3×#10598993, #14289118, …
maximal quotient ofC3×#10614061, C3×#10605187, C3×D4×C4⋊Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9761);