Finite Group Databasebeta

← Prev (#32912476) Next (#32912478) →

C7×C29×D45 #32912477

order18270
automorphism?
homologyAbelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC7×C29×D45
unambiguous semidirect productC5⋊(C7×D9×C29)
unambiguous semidirect productC9⋊(C7×D5×C29)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C2
derived, HallC5×C9 ⋊ C2×C7×C29
HallC7×C9×C29 ⋊ D5
HallC5×C9×C29 ⋊ C2×C7
HallC5×C7×C29 ⋊ D9
HallC5×C7×C9 ⋊ C2×C29
HallC9×C29 ⋊ C7×D5
HallC5×C29 ⋊ C7×D9
HallC7×C9 ⋊ D5×C29
HallC5×C7 ⋊ D9×C29
SylowC9 ⋊ C7×D5×C29
SylowC5 ⋊ C7×D9×C29

Subgroups

subgroupG/H
center, hypercenterC7×C29D45
commutator, cosocle, hypocenterC5×C9C2×C7×C29
FrattiniC3C7×C29×D15
FittingC5×C7×C9×C29C2
socleC3×C5×C7×C29D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D29×D45, D7×C29×D45, D45×D203, …
maximal normal subgroup ofC7×D29×D45, D7×C29×D45, D45×D203, …
maximal quotient ofC7×C29×Dic45, C2×C7×C29×D45

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 15);