Finite Group Databasebeta

← Prev (#44527573) Next (#44527575) →

C7×(C13⋊C9)⋊D19 #44527574

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C13⋊C9)⋊D19
unambiguous semidirect product(C13⋊C9)⋊(C7×D19)

Splittings

derived, HallC13×C19 ⋊ C2×C7×C9
HallC7×C19×C13⋊C9 ⋊ C2
HallC7×D247 ⋊ C9
HallC19×C13⋊C9 ⋊ C2×C7
HallC7×C13×C19 ⋊ C2×C9
HallC7×C13⋊C9 ⋊ D19
HallD247 ⋊ C7×C9
HallC7×C19 ⋊ D13⋊C9
HallC13⋊C9 ⋊ C7×D19
HallC7×C13 ⋊ C9×D19
SylowC19 ⋊ C7×D13⋊C9
SylowC13 ⋊ C7×C9×D19

Subgroups

subgroupG/H
center, hypercenterC3×C7(C13⋊C3)⋊D19
commutator, hypocenterC13×C19C2×C7×C9
FrattiniC3C7×(C13⋊C3)⋊D19
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C7×D247C3
cosocleC3×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

1491 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 57);