Finite Group Databasebeta

← Prev (#37556060) Next (#37556062) →

C2×C9×D655 #37556061

order23580
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D655
unambiguous semidirect product(C2×C5)⋊(C9×D131)
unambiguous semidirect product(C2×C131)⋊(C9×D5)

Splittings

FittingC2×C5×C9×C131 ⋊ C2
derived, HallC5×C131 ⋊ C22×C9
HallC5×C9×C131 ⋊ C22
HallC9×C131 ⋊ C2×D5
SylowC131 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×D131
SylowC5 ⋊ C2×C9×D131

Subgroups

subgroupG/H
center, hypercenterC2×C9D655
commutator, hypocenterC5×C131C22×C9
FrattiniC3C2×C3×D655
FittingC2×C5×C9×C131C2
socleC2×C3×C5×C131C2×C3
prime radicalC2×C3×D655C3
cosocleC3×C5×C131C22×C3
LCSG ▷ C5×C131
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11790

Conjugacy classes & character table

5922 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 36);