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C5×C9⋊(D41⋊C5) #32914366

order18450
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C9⋊(D41⋊C5)
unambiguous semidirect productC9⋊(C5×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(C5×D9)
unambiguous semidirect productD369⋊C52
unambiguous semidirect product(C5×D369)⋊C5

Splittings

FittingC5×C9×C41 ⋊ C2×C5
derived, HallC9×C41 ⋊ C2×C52
HallC5×C9×C41⋊C5 ⋊ C2
HallC5×C41⋊C5 ⋊ D9
HallD369 ⋊ C52
SylowC41 ⋊ C52×D9
SylowC9 ⋊ C5×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C9⋊(D41⋊C5)
commutator, cosocle, hypocenterC9×C41C2×C52
FrattiniC3C5×C3⋊(D41⋊C5)
FittingC5×C9×C41C2×C5
socleC3×C5×C41C5×D3
LCSG ▷ C9×C41
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1845

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D9×D41⋊C5, D5×C9⋊(D41⋊C5), D45⋊(D41⋊C5), …
maximal normal subgroup ofC5×D9×D41⋊C5, D5×C9⋊(D41⋊C5), D45⋊(D41⋊C5), …
maximal quotient ofC5×C9⋊(Dic41⋊C5), C2×C5×C9⋊(D41⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18450, 35);