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C2×C9×D41⋊C5 #20301540

order7380
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D41⋊C5
unambiguous semidirect productD41⋊(C2×C5×C9)
unambiguous semidirect product(C2×D41)⋊(C5×C9)
unambiguous semidirect product(C41⋊C5)⋊(C22×C9)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C9)
unambiguous semidirect product(C2×C9×D41)⋊C5

Splittings

FittingC2×C9×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C5×C9
HallC9×C41⋊C5 ⋊ C22
HallC2×C9×D41 ⋊ C5
HallC9×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C22×C9
HallC2×D41 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9D41⋊C5
commutator, hypocenterC41C22×C5×C9
FrattiniC3C2×C3×D41⋊C5
FittingC2×C9×C41C2×C5
socleC2×C3×C41C2×C3×C5
LCSG ▷ C41
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×D5×D41⋊C5, C2×C5×C9×D41⋊C5, C2×C9×C5⋊(D41⋊C5)
maximal normal subgroup ofC2×C5×C9×D41⋊C5
maximal quotient ofC2×C9×D41⋊C25, C9×D5×D41⋊C5, C2×C5×C9×D41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 18);