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C5×D9×D59 #24902870

order10620
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D9×D59
unambiguous semidirect product(D9×C59)⋊(C2×C5)
unambiguous semidirect product(C9×D59)⋊(C2×C5)
unambiguous semidirect productD531⋊(C2×C5)

Splittings

Fitting, HallC5×C9×C59 ⋊ C22
derived, HallC9×C59 ⋊ C22×C5
HallC5×C59 ⋊ C2×D9
SylowC59 ⋊ C2×C5×D9
HallC5×C9 ⋊ C2×D59
SylowC9 ⋊ C2×C5×D59

Subgroups

subgroupG/H
center, hypercenterC5D9×D59
commutator, cosocle, hypocenterC9×C59C22×C5
FrattiniC3C5×D3×D59
FittingC5×C9×C59C22
socleC3×C5×C59C2×D3
LCSG ▷ C9×C59
UCSC1 ◁ C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

930 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10620, 13);