Finite Group Databasebeta

← Prev (#34086132) Next (#34086134) →

C5×C31×D7⋊C9 #34086133

order19530
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31×D7⋊C9
unambiguous semidirect productD7⋊(C5×C9×C31)
unambiguous semidirect product(C7⋊C9)⋊(C2×C5×C31)
unambiguous semidirect product(C5×D7)⋊(C9×C31)

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C31
HallC5×C31×C7⋊C9 ⋊ C2
HallC5×D7×C31 ⋊ C9
HallC31×C7⋊C9 ⋊ C2×C5
HallC5×C7×C31 ⋊ C2×C9
HallD7×C31 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ C2×C31
HallC7×C31 ⋊ C2×C5×C9
HallC5×D7 ⋊ C9×C31
HallC7⋊C9 ⋊ C2×C5×C31
HallC5×C7 ⋊ C2×C9×C31
HallD7 ⋊ C5×C9×C31

Subgroups

subgroupG/H
center, hypercenterC3×C5×C31AGL(1,𝔽7)
commutator, hypocenterC7C2×C5×C9×C31
FrattiniC3C5×C31×AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C31C2×C3
prime radicalC3×C5×D7×C31C3
cosocleC3×C7C2×C3×C5×C31
LCSG ▷ C7
UCSC1 ◁ C3×C5×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

3255 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 38);