Finite Group Databasebeta

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C3×C5×#888 #13087900

order1440
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#888

Splittings

HallC32×C5 ⋊ C4⋊Q8
SylowC32 ⋊ C5×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C3×C5C22×D3
commutator, cosocleC22×C3C23×C3×C5
FrattiniC22C22×C3×C5×D3
FittingC32×C5×C4⋊C4C2
socle, prime radicalC22×C32×C5C23
hypercenterC3×C5×C4⋊C4D3
hypocenterC3C3×C5×C4⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C5 ◁ C3×C5×C4⋊C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4217);