Finite Group Databasebeta

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C3×C5×D4×A4 #13089435

order1440
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×C5×D4×A4
unambiguous semidirect productC4⋊(C2×C3×C5×A4)
unambiguous semidirect product(C22×D4)⋊(C32×C5)
unambiguous semidirect product(C22×C3×D4)⋊(C3×C5)
unambiguous semidirect product(C22×C5×D4)⋊C32
unambiguous semidirect product(C22×C3×C5×D4)⋊C3

Splittings

FittingC22×C3×C5×D4 ⋊ C3
HallC22×C5×D4 ⋊ C32
SylowC22×D4 ⋊ C32×C5

Subgroups

subgroupG/H
centerC2×C3×C5C22×A4
commutator, cosocleC23C22×C32×C5
FrattiniC2C22×C3×C5×A4
FittingC22×C3×C5×D4C3
socleC23×C3×C5C22×C3
hypercenterC3×C5×D4A4
hypocenterC22C32×C5×D4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3×C5 ◁ C3×C5×D4

328 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

300 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5752);