Finite Group Databasebeta

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D13×C3⋊D105 #30655693

order16380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productD13×C3⋊D105
unambiguous semidirect product(C3×D13)⋊D105
unambiguous semidirect product(C5×D13)⋊(C3⋊D21)
unambiguous semidirect product(C7×D13)⋊(C3⋊D15)

Splittings

Fitting, socle, derived, HallC32×C5×C7×C13 ⋊ C22
HallC32×C7×C13 ⋊ C2×D5
HallC32×C5×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D13
HallC32×C13 ⋊ C2×D35
HallC7×C13 ⋊ C2×C3⋊D15
HallC5×C13 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ D5×D13
HallC32×C5 ⋊ D7×D13
HallC5×C7 ⋊ C3⋊D3×D13
SylowC13 ⋊ C2×C3⋊D105
SylowC32 ⋊ D13×D35
SylowC7 ⋊ D13×C3⋊D15
SylowC5 ⋊ D13×C3⋊D21

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C13C22
LCSG ▷ C32×C5×C7×C13
UCSC1

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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, 743);