Finite Group Databasebeta

← Prev (#34086114) Next (#34086116) →

C5×C31×D63 #34086115

order19530
automorphism?
homologyAbelianization (H1) = C2×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31×D63
unambiguous semidirect productC7⋊(C5×D9×C31)
unambiguous semidirect productC9⋊(C5×D7×C31)

Splittings

Fitting, HallC5×C7×C9×C31 ⋊ C2
derived, HallC7×C9 ⋊ C2×C5×C31
HallC7×C9×C31 ⋊ C2×C5
HallC5×C9×C31 ⋊ D7
HallC5×C7×C31 ⋊ D9
HallC5×C7×C9 ⋊ C2×C31
HallC9×C31 ⋊ C5×D7
HallC7×C31 ⋊ C5×D9
HallC5×C9 ⋊ D7×C31
HallC5×C7 ⋊ D9×C31
SylowC9 ⋊ C5×D7×C31
SylowC7 ⋊ C5×D9×C31

Subgroups

subgroupG/H
center, hypercenterC5×C31D63
commutator, cosocle, hypocenterC7×C9C2×C5×C31
FrattiniC3C5×C31×D21
FittingC5×C7×C9×C31C2
socleC3×C5×C7×C31D3
LCSG ▷ C7×C9
UCSC1 ◁ C5×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

5115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 20);