Finite Group Databasebeta

← Prev (#35207290) Next (#35207292) →

C5×D229⋊C9 #35207291

order20610
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D229⋊C9
unambiguous semidirect productD229⋊(C5×C9)
unambiguous semidirect product(C229⋊C9)⋊(C2×C5)
unambiguous semidirect product(C5×D229)⋊C9

Splittings

derived, SylowC229 ⋊ C2×C5×C9
HallC5×C229⋊C9 ⋊ C2
HallC5×D229 ⋊ C9
HallC229⋊C9 ⋊ C2×C5
HallC5×C229 ⋊ C2×C9
HallD229 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5D229⋊C3
commutator, hypocenterC229C2×C5×C9
FrattiniC3C5×D229⋊C3
Fitting, socleC3×C5×C229C2×C3
prime radicalC3×C5×D229C3
cosocleC3×C229C2×C3×C5
LCSG ▷ C229
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10305

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20610, 10);