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C5×D7×D117 #30655128

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

Aliases

direct productC5×D7×D117
unambiguous semidirect product(C9×D7)⋊(C5×D13)
unambiguous semidirect product(C13×D7)⋊(C5×D9)

Splittings

Fitting, HallC5×C7×C9×C13 ⋊ C22
derived, HallC7×C9×C13 ⋊ C22×C5
HallC5×C9×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D13
HallC9×C13 ⋊ C2×C5×D7
HallC7×C13 ⋊ C2×C5×D9
HallC5×C13 ⋊ D7×D9
HallC7×C9 ⋊ C2×C5×D13
HallC5×C9 ⋊ D7×D13
HallC5×C7 ⋊ C2×D117
SylowC13 ⋊ C5×D7×D9
SylowC9 ⋊ C5×D7×D13
SylowC7 ⋊ C2×C5×D117

Subgroups

subgroupG/H
center, hypercenterC5D7×D117
commutator, cosocle, hypocenterC7×C9×C13C22×C5
FrattiniC3C5×D7×D39
FittingC5×C7×C9×C13C22
socleC3×C5×C7×C13C2×D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C5

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 178);