Finite Group Databasebeta

← Prev (#44539810) Next (#44539812) →

C7×D29×D13⋊C3 #44539811

order31668
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D29×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×D29)

Splittings

Fitting, socle, HallC7×C13×C29 ⋊ C22×C3
derived, HallC13×C29 ⋊ C22×C3×C7
HallC7×D13×D29 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C22
HallD13×D29 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D29
HallC7×C29 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D29
HallC13⋊C3 ⋊ C2×C7×D29
SylowC29 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D29

Subgroups

subgroupG/H
center, hypercenterC7D29×D13⋊C3
commutator, cosocle, hypocenterC13×C29C22×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C29C22×C3
LCSG ▷ C13×C29
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2639

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 106);