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C5×C29⋊(D7⋊C9) #32912490

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

Aliases

direct productC5×C29⋊(D7⋊C9)
unambiguous semidirect productC29⋊(C5×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C5×D29)
unambiguous semidirect productD203⋊(C5×C9)
unambiguous semidirect product(C5×D203)⋊C9

Splittings

derived, HallC7×C29 ⋊ C2×C5×C9
HallC5×C29×C7⋊C9 ⋊ C2
HallC5×D203 ⋊ C9
HallC29×C7⋊C9 ⋊ C2×C5
HallC5×C7×C29 ⋊ C2×C9
HallD203 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ D29
HallC5×C29 ⋊ D7⋊C9
HallC7⋊C9 ⋊ C5×D29
HallC5×C7 ⋊ C9×D29
SylowC29 ⋊ C5×D7⋊C9
SylowC7 ⋊ C5×C9×D29

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D29
commutator, hypocenterC7×C29C2×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)⋊D29
Fitting, socleC3×C5×C7×C29C2×C3
prime radicalC3×C5×D203C3
cosocleC3×C7×C29C2×C3×C5
LCSG ▷ C7×C29
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D29×D7⋊C9, D5×C29⋊(D7⋊C9), D145⋊(D7⋊C9), …
maximal normal subgroup ofC5×D29×D7⋊C9, D5×C29⋊(D7⋊C9), D145⋊(D7⋊C9), …
maximal quotient ofC5×(C7⋊C9)⋊Dic29, C2×C5×C29⋊(D7⋊C9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 28);