Finite Group Databasebeta

← Prev (#30655147) Next (#30655149) →

C7×D5×D117 #30655148

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

Aliases

direct productC7×D5×D117
unambiguous semidirect product(C9×D5)⋊(C7×D13)
unambiguous semidirect product(D5×C13)⋊(C7×D9)

Splittings

Fitting, HallC5×C7×C9×C13 ⋊ C22
derived, HallC5×C9×C13 ⋊ C22×C7
HallC7×C9×C13 ⋊ C2×D5
HallC5×C7×C13 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D13
HallC9×C13 ⋊ C2×C7×D5
HallC7×C13 ⋊ D5×D9
HallC5×C13 ⋊ C2×C7×D9
HallC7×C9 ⋊ D5×D13
HallC5×C9 ⋊ C2×C7×D13
HallC5×C7 ⋊ C2×D117
SylowC13 ⋊ C7×D5×D9
SylowC9 ⋊ C7×D5×D13
SylowC5 ⋊ C2×C7×D117

Subgroups

subgroupG/H
center, hypercenterC7D5×D117
commutator, cosocle, hypocenterC5×C9×C13C22×C7
FrattiniC3C7×D5×D39
FittingC5×C7×C9×C13C22
socleC3×C5×C7×C13C2×D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C7

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 198);