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C5×C9⋊#10624382 #45656378

order32580
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊#10624382
unambiguous semidirect productC9⋊(C5×#10624382)

Splittings

Fitting, HallC5×C9×C181 ⋊ C4
derived, HallC9×C181 ⋊ C4×C5
HallC5×C181 ⋊ Dic9
SylowC181 ⋊ C5×Dic9
HallC5×C9 ⋊ #10624382
SylowC9 ⋊ C5×#10624382

Subgroups

subgroupG/H
center, hypercenterC5C9⋊#10624382
commutator, hypocenterC9×C181C4×C5
FrattiniC3C5×C3⋊#10624382
FittingC5×C9×C181C4
socleC3×C5×C181Dic3
prime radicalC3×C5×D181D3
cosocleC9×D181C2×C5
LCSG ▷ C9×C181
UCSC1 ◁ C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 49);