Finite Group Databasebeta

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C3×C5×#877 #13087888

order1440
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×C5×#877

Splittings

HallC32×C5 ⋊ #117
SylowC32 ⋊ C5×#117

Subgroups

subgroupG/H
centerC22×C3×C5C22×D3
commutatorC2×C3C22×C3×C4×C5
FrattiniC22C22×C3×C5×D3
FittingC32×C5×C22⋊C4C2
socleC22×C32×C5C23
prime radicalC23×C32×C5C22
cosocleC22×C3C23×C3×C5
hypercenterC3×C5×C22⋊C4D3
hypocenterC3C3×C5×#117
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C5 ◁ C3×C5×C22⋊C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4205);