Finite Group Databasebeta

C7×C19×D13⋊C9 #44527561

order31122
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19×D13⋊C9
unambiguous semidirect productD13⋊(C7×C9×C19)
unambiguous semidirect product(C13⋊C9)⋊(C2×C7×C19)

Splittings

derived, SylowC13 ⋊ C2×C7×C9×C19
HallC7×C19×C13⋊C9 ⋊ C2
HallC7×C19×D13 ⋊ C9
HallC19×C13⋊C9 ⋊ C2×C7
HallC7×C13×C19 ⋊ C2×C9
HallC7×C13⋊C9 ⋊ C2×C19
HallC19×D13 ⋊ C7×C9
HallC13×C19 ⋊ C2×C7×C9
HallC7×D13 ⋊ C9×C19
HallC13⋊C9 ⋊ C2×C7×C19
HallC7×C13 ⋊ C2×C9×C19
HallD13 ⋊ C7×C9×C19

Subgroups

subgroupG/H
center, hypercenterC3×C7×C19D13⋊C3
commutator, hypocenterC13C2×C7×C9×C19
FrattiniC3C7×C19×D13⋊C3
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C7×C19×D13C3
cosocleC3×C13C2×C3×C7×C19
LCSG ▷ C13
UCSC1 ◁ C3×C7×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

3192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 44);