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C5×C9⋊(D29⋊C7) #32912485

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊(D29⋊C7)
unambiguous semidirect productC9⋊(C5×D29⋊C7)
unambiguous semidirect product(C29⋊C7)⋊(C5×D9)
unambiguous semidirect productD261⋊(C5×C7)
unambiguous semidirect product(C5×D261)⋊C7

Splittings

Fitting, HallC5×C9×C29 ⋊ C2×C7
derived, HallC9×C29 ⋊ C2×C5×C7
HallC5×C9×C29⋊C7 ⋊ C2
HallC5×D261 ⋊ C7
HallC9×C29⋊C7 ⋊ C2×C5
HallC5×C29⋊C7 ⋊ D9
HallD261 ⋊ C5×C7
HallC29⋊C7 ⋊ C5×D9
HallC5×C29 ⋊ C7×D9
HallC5×C9 ⋊ D29⋊C7
SylowC29 ⋊ C5×C7×D9
SylowC9 ⋊ C5×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC5C9⋊(D29⋊C7)
commutator, cosocle, hypocenterC9×C29C2×C5×C7
FrattiniC3C5×C3⋊(D29⋊C7)
FittingC5×C9×C29C2×C7
socleC3×C5×C29D3×C7
LCSG ▷ C9×C29
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D9×D29⋊C7, D5×C9⋊(D29⋊C7), D45⋊(D29⋊C7), …
maximal normal subgroup ofC5×D9×D29⋊C7, D5×C9⋊(D29⋊C7), D45⋊(D29⋊C7), …
maximal quotient ofC5×C9⋊(Dic29⋊C7), C2×C5×C9⋊(D29⋊C7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 23);