Finite Group Databasebeta

← Prev (#34062868) Next (#34062870) →

C2×C41×D13⋊C9 #34062869

order19188
automorphism?
homologyAbelianization (H1) = C22×C9×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×D13⋊C9
unambiguous semidirect productD13⋊(C2×C9×C41)
unambiguous semidirect product(C2×D13)⋊(C9×C41)
unambiguous semidirect product(C13⋊C9)⋊(C22×C41)
unambiguous semidirect product(C2×C13⋊C9)⋊(C2×C41)
unambiguous semidirect product(C2×D13×C41)⋊C9

Splittings

derived, SylowC13 ⋊ C22×C9×C41
HallC41×C13⋊C9 ⋊ C22
HallC2×D13×C41 ⋊ C9
HallC13×C41 ⋊ C22×C9
HallC13⋊C9 ⋊ C22×C41
HallC2×D13 ⋊ C9×C41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C41D13⋊C3
commutator, hypocenterC13C22×C9×C41
FrattiniC3C2×C41×D13⋊C3
Fitting, socleC2×C3×C13×C41C2×C3
prime radicalC2×C3×D13×C41C3
cosocleC3×C13C22×C3×C41
LCSG ▷ C13
UCSC1 ◁ C2×C3×C41

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9594

Conjugacy classes & character table

1968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 21);