Finite Group Databasebeta

← Prev (#30655143) Next (#30655145) →

D7×D585 #30655144

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

Aliases

direct productD7×D585
unambiguous semidirect product(C5×D7)⋊D117
unambiguous semidirect product(C9×D7)⋊D65
unambiguous semidirect product(C13×D7)⋊D45

Splittings

Fitting, derived, HallC5×C7×C9×C13 ⋊ C22
HallC7×C9×C13 ⋊ C2×D5
HallC5×C9×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D13
HallC9×C13 ⋊ D5×D7
HallC7×C13 ⋊ C2×D45
HallC5×C13 ⋊ D7×D9
HallC7×C9 ⋊ C2×D65
HallC5×C9 ⋊ D7×D13
HallC5×C7 ⋊ C2×D117
SylowC13 ⋊ D7×D45
SylowC9 ⋊ D7×D65
SylowC7 ⋊ C2×D585
SylowC5 ⋊ D7×D117

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C7×C9×C13C22
FrattiniC3D7×D195
socleC3×C5×C7×C13C2×D3
LCSG ▷ C5×C7×C9×C13
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 194);