Finite Group Databasebeta

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C4×C5×D4×A4 #14511311

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC4×C5×D4×A4
unambiguous semidirect product(C22×C4×D4)⋊(C3×C5)
unambiguous semidirect product(C22×C4×C5×D4)⋊C3

Splittings

Fitting, HallC22×C4×C5×D4 ⋊ C3
SylowC22×C4×D4 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C4×C5C22×A4
commutatorC23C22×C3×C4×C5
FrattiniC22C23×C5×A4
FittingC22×C4×C5×D4C3
socleC24×C5C23×C3
prime radicalC2×C5×D4×A4C2
cosocleC24C23×C3×C5
hypercenterC4×C5×D4A4
hypocenterC22C3×C4×C5×D4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C4×C5 ◁ C4×C5×D4

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237009);