Finite Group Databasebeta

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C3×#65688 #11752221

order960
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#65688

Splittings

FittingC3×C42×C5 ⋊ C4
HallC3×C5 ⋊ #384
SylowC5 ⋊ C3×#384

Subgroups

subgroupG/H
centerC22×C3C22×AGL(1,𝔽5)
commutatorC22×C5C22×C3×C4
FrattiniC22C22×C3×AGL(1,𝔽5)
FittingC3×C42×C5C4
socleC22×C3×C5C22×C4
prime radicalC22×C3×D5C23
cosocleC22×D5C23×C3
hypercenterC3×C42AGL(1,𝔽5)
hypocenterC5C3×#384
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42

372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2,3)(4,5,6,8,7)(13,14,15,16);(9,10,11,12);(5,6,7,8)(10,12)(14,16)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10598586, #14277183, C3×#10604417, …
maximal normal subgroup ofC3×#10598586, #14277183, C3×#10604417, …
maximal quotient ofC3×#10604198, C3×#10603804, C3×#10604190, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 6416);