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C5×D9×C41⋊C5 #32914367

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

Aliases

direct productC5×D9×C41⋊C5
unambiguous semidirect productC9⋊(C2×C5×C41⋊C5)
unambiguous semidirect product(D9×C41)⋊C52
unambiguous semidirect product(C5×D9×C41)⋊C5

Splittings

FittingC5×C9×C41 ⋊ C2×C5
derived, HallC9×C41 ⋊ C2×C52
HallC5×C9×C41⋊C5 ⋊ C2
HallD9×C41 ⋊ C52
SylowC41 ⋊ C52×D9
SylowC9 ⋊ C2×C5×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC5D9×C41⋊C5
commutator, cosocle, hypocenterC9×C41C2×C52
FrattiniC3C5×D3×C41⋊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

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

Relationships

maximal subgroup ofC5×D9×D41⋊C5, D9×C5⋊(D41⋊C5), D5×D9×C41⋊C5, …
maximal normal subgroup ofC5×D9×D41⋊C5, D9×C5⋊(D41⋊C5), D5×D9×C41⋊C5, …
maximal quotient ofC5×Dic9×C41⋊C5, C2×C5×D9×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18450, 36);