Finite Group Databasebeta

← Prev (#49144071) Next (#49144073) →

D13×D705 #49144072

order36660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD13×D705
unambiguous semidirect product(C3×D13)⋊D235
unambiguous semidirect product(C5×D13)⋊D141
unambiguous semidirect product(D13×C47)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C13×C47 ⋊ C22
HallC5×C13×C47 ⋊ C2×D3
HallC3×C13×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C2×D13
HallC13×C47 ⋊ C2×D15
HallC5×C47 ⋊ D3×D13
HallC3×C5×C13 ⋊ C2×D47
HallC3×C47 ⋊ D5×D13
HallC5×C13 ⋊ C2×D141
SylowC47 ⋊ D13×D15
HallC3×C13 ⋊ C2×D235
HallC3×C5 ⋊ D13×D47
SylowC13 ⋊ C2×D705
SylowC5 ⋊ D13×D141
SylowC3 ⋊ D13×D235

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C47C22
LCSG ▷ C3×C5×C13×C47
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9165

Conjugacy classes & character table

2832 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 92);