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D13×D615 #44544464

order31980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD13×D615
unambiguous semidirect product(C3×D13)⋊D205
unambiguous semidirect product(C5×D13)⋊D123
unambiguous semidirect product(D13×C41)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C13×C41 ⋊ C22
HallC5×C13×C41 ⋊ C2×D3
HallC3×C13×C41 ⋊ C2×D5
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×D15
HallC5×C41 ⋊ D3×D13
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ D5×D13
HallC5×C13 ⋊ C2×D123
SylowC41 ⋊ D13×D15
HallC3×C13 ⋊ C2×D205
HallC3×C5 ⋊ D13×D41
SylowC13 ⋊ C2×D615
SylowC5 ⋊ D13×D123
SylowC3 ⋊ D13×D205

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C41C22
LCSG ▷ C3×C5×C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 192);