Finite Group Databasebeta

← Prev (#44535602) Next (#44535604) →

C2×C67×D13⋊C9 #44535603

order31356
automorphism?
homologyAbelianization (H1) = C22×C9×C67 · Schur multiplier (H2) = C2

Aliases

direct productC2×C67×D13⋊C9
unambiguous semidirect productD13⋊(C2×C9×C67)
unambiguous semidirect product(C2×D13)⋊(C9×C67)
unambiguous semidirect product(C13⋊C9)⋊(C22×C67)
unambiguous semidirect product(C2×C13⋊C9)⋊(C2×C67)

Splittings

derived, SylowC13 ⋊ C22×C9×C67
HallC67×C13⋊C9 ⋊ C22
HallC2×D13×C67 ⋊ C9
HallC13×C67 ⋊ C22×C9
HallC13⋊C9 ⋊ C22×C67
HallC2×D13 ⋊ C9×C67

Subgroups

subgroupG/H
center, hypercenterC2×C3×C67D13⋊C3
commutator, hypocenterC13C22×C9×C67
FrattiniC3C2×C67×D13⋊C3
Fitting, socleC2×C3×C13×C67C2×C3
prime radicalC2×C3×D13×C67C3
cosocleC3×C13C22×C3×C67
LCSG ▷ C13
UCSC1 ◁ C2×C3×C67

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15678

Conjugacy classes & character table

3216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 39);