Finite Group Databasebeta

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C5×C7×A4×C13⋊C3 #30655547

order16380
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C7×A4×C13⋊C3
unambiguous semidirect product(C22×C13⋊C3)⋊(C3×C5×C7)
unambiguous semidirect product(A4×C13)⋊(C3×C5×C7)
unambiguous semidirect product(C22⋊(C13⋊C3))⋊(C3×C5×C7)
unambiguous semidirect product(C22×C5×C13⋊C3)⋊(C3×C7)
unambiguous semidirect product(C5×A4×C13)⋊(C3×C7)
unambiguous semidirect product(C5×C22⋊(C13⋊C3))⋊(C3×C7)

Splittings

Fitting, socle, HallC22×C5×C7×C13 ⋊ C32
derived, HallC22×C13 ⋊ C32×C5×C7
HallC5×C7×C13 ⋊ C3×A4
HallC22×C7×C13 ⋊ C32×C5
HallC22×C5×C13 ⋊ C32×C7
HallC22×C5×C7 ⋊ C3×C13⋊C3
HallC7×C13 ⋊ C3×C5×A4
HallC5×C13 ⋊ C3×C7×A4
HallC22×C7 ⋊ C3×C5×C13⋊C3
HallC22×C5 ⋊ C3×C7×C13⋊C3
SylowC13 ⋊ C3×C5×C7×A4
SylowC22 ⋊ C3×C5×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C7A4×C13⋊C3
commutator, cosocle, hypocenterC22×C13C32×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C13C32
LCSG ▷ C22×C13
UCSC1 ◁ C5×C7

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 597);