Finite Group Databasebeta

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C5×C9×C29⋊C7 #22603689

order9135
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C29⋊C7
unambiguous semidirect productC29⋊(C5×C7×C9)
unambiguous semidirect product(C5×C29)⋊(C7×C9)
unambiguous semidirect product(C9×C29)⋊(C5×C7)
unambiguous semidirect product(C5×C9×C29)⋊C7

Splittings

Fitting, HallC5×C9×C29 ⋊ C7
derived, SylowC29 ⋊ C5×C7×C9
HallC9×C29 ⋊ C5×C7
HallC5×C29 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9C29⋊C7
commutator, hypocenterC29C5×C7×C9
FrattiniC3C3×C5×C29⋊C7
FittingC5×C9×C29C7
socleC3×C5×C29C3×C7
LCSG ▷ C29
UCSC1 ◁ C5×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

495 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C9×C29⋊C7, C5×C9×D29⋊C7, C9×D5×C29⋊C7, …
maximal normal subgroup ofC2×C5×C9×C29⋊C7, C5×C9×D29⋊C7, C9×D5×C29⋊C7, …
maximal quotient ofC2×C5×C9×C29⋊C7, C5×C22⋊C9×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9135, 2);