Finite Group Databasebeta

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C5×A4×C22⋊Q8 #14511323

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

Aliases

direct productC5×A4×C22⋊Q8
unambiguous semidirect product(C22×C22⋊Q8)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C22⋊Q8)⋊C3

Splittings

Fitting, HallC22×C5×C22⋊Q8 ⋊ C3
SylowC22×C22⋊Q8 ⋊ C3×C5

Subgroups

subgroupG/H
centerC22×C5C23×A4
commutator, cosocleC24C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×C22⋊Q8C3
socleC24×C5C23×C3
prime radicalC23×C5×A4C22
hypercenterC5×C22⋊Q8A4
hypocenterC22C3×C5×C22⋊Q8
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C5 ◁ C5×C22⋊Q8

860 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, 237021);