Finite Group Databasebeta

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C5×A4×D12 #13089102

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

Aliases

direct productC5×A4×D12
unambiguous semidirect productC4⋊(C5×D3×A4)
unambiguous semidirect product(C22×D12)⋊(C3×C5)
unambiguous semidirect product(C22×C5×D12)⋊C3

Splittings

FittingC22×C3×C4×C5 ⋊ C2×C3

Subgroups

subgroupG/H
centerC2×C5C2×D3×A4
commutator, cosocleC23×C3C22×C3×C5
FrattiniC2C2×C5×D3×A4
FittingC22×C3×C4×C5C2×C3
socleC23×C3×C5C22×C3
hypercenterC4×C5D3×A4
hypocenterC22×C3C3×C5×D4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C5 ◁ C4×C5

276 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 54 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

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5419);