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C5×C9×D355 #44544051

order31950
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D355
unambiguous semidirect productC5⋊(C5×C9×D71)

Splittings

Fitting, HallC52×C9×C71 ⋊ C2
derivedC5×C71 ⋊ C2×C5×C9
HallC52×C71 ⋊ C2×C9
HallC9×C71 ⋊ C5×D5
HallC52×C9 ⋊ D71
SylowC71 ⋊ C5×C9×D5
SylowC52 ⋊ C9×D71

Subgroups

subgroupG/H
center, hypercenterC5×C9D355
commutator, hypocenterC5×C71C2×C5×C9
FrattiniC3C3×C5×D355
FittingC52×C9×C71C2
socleC3×C52×C71C2×C3
prime radicalC3×C5×D355C3
cosocleC3×C5×C71C2×C3×C5
LCSG ▷ C5×C71
UCSC1 ◁ C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6390

Conjugacy classes & character table

8055 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 54);