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C5×C9×D29⋊C7 #32912481

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D29⋊C7
unambiguous semidirect productD29⋊(C5×C7×C9)
unambiguous semidirect product(C29⋊C7)⋊(C2×C5×C9)
unambiguous semidirect product(C5×D29)⋊(C7×C9)
unambiguous semidirect product(C9×D29)⋊(C5×C7)
unambiguous semidirect product(C5×C9×D29)⋊C7

Splittings

Fitting, HallC5×C9×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C5×C7×C9
HallC5×C9×C29⋊C7 ⋊ C2
HallC5×C9×D29 ⋊ C7
HallC9×C29⋊C7 ⋊ C2×C5
HallC5×C29⋊C7 ⋊ C2×C9
HallC9×D29 ⋊ C5×C7
HallC5×D29 ⋊ C7×C9
HallC9×C29 ⋊ C2×C5×C7
HallC29⋊C7 ⋊ C2×C5×C9
HallC5×C29 ⋊ C2×C7×C9
HallD29 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9D29⋊C7
commutator, hypocenterC29C2×C5×C7×C9
FrattiniC3C3×C5×D29⋊C7
FittingC5×C9×C29C2×C7
socleC3×C5×C29C2×C3×C7
prime radicalC3×C5×D29⋊C7C3
cosocleC3×C29C2×C3×C5×C7
LCSG ▷ C29
UCSC1 ◁ C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C9×AGL(1,𝔽29), C9×#10596817⋊C7, C9×D5×D29⋊C7, …
maximal normal subgroup ofC5×C9×AGL(1,𝔽29), C9×#10596817⋊C7, C9×D5×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, 19);