Finite Group Databasebeta

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C5×D337⋊C9 #44476756

order30330
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D337⋊C9
unambiguous semidirect productD337⋊(C5×C9)
unambiguous semidirect product(C337⋊C9)⋊(C2×C5)
unambiguous semidirect product(C5×D337)⋊C9

Splittings

derived, SylowC337 ⋊ C2×C5×C9
HallC5×C337⋊C9 ⋊ C2
HallC5×D337 ⋊ C9
HallC337⋊C9 ⋊ C2×C5
HallC5×C337 ⋊ C2×C9
HallD337 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5D337⋊C3
commutator, hypocenterC337C2×C5×C9
FrattiniC3C5×D337⋊C3
Fitting, socleC3×C5×C337C2×C3
prime radicalC3×C5×D337C3
cosocleC3×C337C2×C3×C5
LCSG ▷ C337
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15165

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30330, 10);