Finite Group Databasebeta

C9×C31×D35 #34086111

order19530
automorphism?
homologyAbelianization (H1) = C2×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31×D35
unambiguous semidirect productC5⋊(C9×D7×C31)

Splittings

Fitting, HallC5×C7×C9×C31 ⋊ C2
derived, HallC5×C7 ⋊ C2×C9×C31
HallC7×C9×C31 ⋊ D5
HallC5×C9×C31 ⋊ D7
HallC5×C7×C31 ⋊ C2×C9
HallC5×C7×C9 ⋊ C2×C31
HallC7×C31 ⋊ C9×D5
HallC5×C31 ⋊ C9×D7
HallC7×C9 ⋊ D5×C31
HallC5×C9 ⋊ D7×C31
SylowC7 ⋊ C9×D5×C31
SylowC5 ⋊ C9×D7×C31

Subgroups

subgroupG/H
center, hypercenterC9×C31D35
commutator, hypocenterC5×C7C2×C9×C31
FrattiniC3C3×C31×D35
FittingC5×C7×C9×C31C2
socleC3×C5×C7×C31C2×C3
prime radicalC3×C31×D35C3
cosocleC3×C5×C7C2×C3×C31
LCSG ▷ C5×C7
UCSC1 ◁ C9×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

5301 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 16);