Finite Group Databasebeta

← Prev (#45659458) Next (#45659460) →

C5×C9×D365 #45659459

order32850
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D365
unambiguous semidirect productC5⋊(C5×C9×D73)

Splittings

Fitting, HallC52×C9×C73 ⋊ C2
derivedC5×C73 ⋊ C2×C5×C9
HallC52×C73 ⋊ C2×C9
HallC9×C73 ⋊ C5×D5
HallC52×C9 ⋊ D73
SylowC73 ⋊ C5×C9×D5
SylowC52 ⋊ C9×D73

Subgroups

subgroupG/H
center, hypercenterC5×C9D365
commutator, hypocenterC5×C73C2×C5×C9
FrattiniC3C3×C5×D365
FittingC52×C9×C73C2
socleC3×C52×C73C2×C3
prime radicalC3×C5×D365C3
cosocleC3×C5×C73C2×C3×C5
LCSG ▷ C5×C73
UCSC1 ◁ C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6570

Conjugacy classes & character table

8280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32850, 62);