Finite Group Databasebeta

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C5×C7×D9×D13 #30655124

order16380
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×D9×D13
unambiguous semidirect product(C13×D9)⋊(C2×C5×C7)
unambiguous semidirect product(C9×D13)⋊(C2×C5×C7)
unambiguous semidirect productD117⋊(C2×C5×C7)

Splittings

Fitting, HallC5×C7×C9×C13 ⋊ C22
derived, HallC9×C13 ⋊ C22×C5×C7
HallC7×C9×C13 ⋊ C22×C5
HallC5×C9×C13 ⋊ C22×C7
HallC5×C7×C13 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D13
HallC7×C13 ⋊ C2×C5×D9
HallC5×C13 ⋊ C2×C7×D9
HallC7×C9 ⋊ C2×C5×D13
HallC5×C9 ⋊ C2×C7×D13
SylowC13 ⋊ C2×C5×C7×D9
SylowC9 ⋊ C2×C5×C7×D13

Subgroups

subgroupG/H
center, hypercenterC5×C7D9×D13
commutator, cosocle, hypocenterC9×C13C22×C5×C7
FrattiniC3C5×D3×C7×D13
FittingC5×C7×C9×C13C22
socleC3×C5×C7×C13C2×D3
LCSG ▷ C9×C13
UCSC1 ◁ C5×C7

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

1680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 174);