Finite Group Databasebeta

← Prev (#44501433) Next (#44501435) →

D3×C7×D5×C73 #44501434

order30660
automorphism?
homologyAbelianization (H1) = C22×C7×C73 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D5×C73
unambiguous semidirect product(C5×D3)⋊(C2×C7×C73)
unambiguous semidirect product(C3×D5)⋊(C2×C7×C73)
unambiguous semidirect productD15⋊(C2×C7×C73)

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C22
derived, HallC3×C5 ⋊ C22×C7×C73
HallC5×C7×C73 ⋊ C2×D3
HallC3×C7×C73 ⋊ C2×D5
HallC3×C5×C73 ⋊ C22×C7
HallC5×C73 ⋊ C2×D3×C7
HallC3×C73 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C22×C73
HallC5×C7 ⋊ C2×D3×C73
HallC3×C7 ⋊ C2×D5×C73
SylowC5 ⋊ C2×D3×C7×C73
SylowC3 ⋊ C2×C7×D5×C73

Subgroups

subgroupG/H
center, hypercenterC7×C73D3×D5
commutator, cosocle, hypocenterC3×C5C22×C7×C73
FrattiniC1G
Fitting, socleC3×C5×C7×C73C22
LCSG ▷ C3×C5
UCSC1 ◁ C7×C73

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

6132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 197);