Finite Group Databasebeta

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C3×C5×A4×C89 #30630896

order16020
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C5×C89 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×A4×C89
unambiguous semidirect productC22⋊(C32×C5×C89)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C89)
unambiguous semidirect product(C22×C5)⋊(C32×C89)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C89)
unambiguous semidirect product(C22×C89)⋊(C32×C5)
unambiguous semidirect product(C22×C3×C89)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C89)⋊C32
unambiguous semidirect product(C22×C3×C5×C89)⋊C3

Splittings

Fitting, socleC22×C3×C5×C89 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C89
HallC22×C5×C89 ⋊ C32
HallC22×C89 ⋊ C32×C5
HallC22×C5 ⋊ C32×C89

Subgroups

subgroupG/H
center, hypercenterC3×C5×C89A4
commutator, cosocle, hypocenterC22C32×C5×C89
FrattiniC1G
Fitting, socleC22×C3×C5×C89C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C89

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5340

Conjugacy classes & character table

5340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 101);