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D45×C41⋊C5 #32914369

order18450
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD45×C41⋊C5
unambiguous semidirect productC5⋊(D9×C41⋊C5)
unambiguous semidirect productC9⋊(D5×C41⋊C5)
unambiguous semidirect product(C41×D45)⋊C5

Splittings

Fitting, derivedC5×C9×C41 ⋊ C2×C5
HallC5×C9×C41⋊C5 ⋊ C2
HallC5×C41⋊C5 ⋊ D9
HallC9×C41 ⋊ C5×D5
SylowC41 ⋊ C5×D45
SylowC9 ⋊ D5×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C9×C41C2×C5
FrattiniC3D15×C41⋊C5
socleC3×C5×C41C5×D3
LCSG ▷ C5×C9×C41
UCSC1

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1845

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD45×D41⋊C5, D45⋊(D41⋊C5), D5×D9×C41⋊C5, …
maximal normal subgroup ofD45×D41⋊C5, D45⋊(D41⋊C5), D5×D9×C41⋊C5, …
maximal quotient ofDic45×C41⋊C5, C2×D45×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18450, 38);