Finite Group Databasebeta

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C5×A4×#121 #14511322

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×A4×#121
unambiguous semidirect product(C22×#121)⋊(C3×C5)
unambiguous semidirect product(C22×C5×#121)⋊C3

Splittings

Fitting, HallC22×C5×#121 ⋊ C3
SylowC22×#121 ⋊ C3×C5

Subgroups

subgroupG/H
centerC22×C5C23×A4
commutator, cosocleC24C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×#121C3
socleC24×C5C23×C3
hypercenterC5×#121A4
hypocenterC22C3×C5×#121
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C5 ◁ C5×#121

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237020);