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C5×C9×C41⋊C5 #22604334

order9225
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×C9×C41⋊C5
unambiguous semidirect productC41⋊(C52×C9)
unambiguous semidirect product(C5×C41)⋊(C5×C9)
unambiguous semidirect product(C9×C41)⋊C52
unambiguous semidirect product(C5×C9×C41)⋊C5

Splittings

FittingC5×C9×C41 ⋊ C5
derived, SylowC41 ⋊ C52×C9
HallC9×C41 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C9C41⋊C5
commutator, hypocenterC41C52×C9
FrattiniC3C3×C5×C41⋊C5
FittingC5×C9×C41C5
socleC3×C5×C41C3×C5
LCSG ▷ C41
UCSC1 ◁ C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

585 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9×D41⋊C5, C9×C5⋊(D41⋊C5), C9×D5×C41⋊C5, …
maximal normal subgroup ofC5×C9×D41⋊C5, C9×C5⋊(D41⋊C5), C9×D5×C41⋊C5, …
maximal quotient ofC2×C5×C9×C41⋊C5, C5×C22⋊C9×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9225, 6);