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C7×D1305 #32912478

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

Aliases

direct productC7×D1305
unambiguous semidirect productC5⋊(C7×D261)
unambiguous semidirect productC9⋊(C7×D145)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C2
derived, HallC5×C9×C29 ⋊ C2×C7
HallC7×C9×C29 ⋊ D5
HallC5×C7×C29 ⋊ D9
HallC5×C7×C9 ⋊ D29
HallC9×C29 ⋊ C7×D5
HallC7×C29 ⋊ D45
HallC5×C29 ⋊ C7×D9
HallC7×C9 ⋊ D145
HallC5×C9 ⋊ C7×D29
HallC5×C7 ⋊ D261
SylowC29 ⋊ C7×D45
SylowC9 ⋊ C7×D145
SylowC5 ⋊ C7×D261

Subgroups

subgroupG/H
center, hypercenterC7D1305
commutator, cosocle, hypocenterC5×C9×C29C2×C7
FrattiniC3C7×D435
FittingC5×C7×C9×C29C2
socleC3×C5×C7×C29D3
LCSG ▷ C5×C9×C29
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4578 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D29×D45, D7×D1305, D203⋊D45, …
maximal normal subgroup ofC7×D29×D45, D7×D1305, D203⋊D45, …
maximal quotient ofC7×Dic1305, C2×C7×D1305

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 16);