Finite Group Databasebeta

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D13×D315 #30655142

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

Aliases

direct productD13×D315
unambiguous semidirect product(C5×D13)⋊D63
unambiguous semidirect product(C7×D13)⋊D45
unambiguous semidirect product(C9×D13)⋊D35

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 ⋊ C2×D35
HallC7×C13 ⋊ C2×D45
HallC5×C13 ⋊ C2×D63
HallC7×C9 ⋊ D5×D13
HallC5×C9 ⋊ D7×D13
HallC5×C7 ⋊ D9×D13
SylowC13 ⋊ C2×D315
SylowC9 ⋊ D13×D35
SylowC7 ⋊ D13×D45
SylowC5 ⋊ D13×D63

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C7×C9×C13C22
FrattiniC3D13×D105
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

1272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 192);