Finite Group Databasebeta

← Prev (#44539882) Next (#44539884) →

C2×C7×C29×D13⋊C3 #44539883

order31668
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C29×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C7×C29)
unambiguous semidirect product(C13⋊C3)⋊(C22×C7×C29)
unambiguous semidirect product(C2×D13)⋊(C3×C7×C29)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C7×C29)

Splittings

Fitting, socleC2×C7×C13×C29 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C7×C29
HallC2×C7×D13×C29 ⋊ C3
HallC7×C29×C13⋊C3 ⋊ C22
HallC7×C13×C29 ⋊ C22×C3
HallC2×D13×C29 ⋊ C3×C7
HallC29×C13⋊C3 ⋊ C22×C7
HallC13×C29 ⋊ C22×C3×C7
HallC2×C7×D13 ⋊ C3×C29
HallC7×C13⋊C3 ⋊ C22×C29
HallC7×C13 ⋊ C22×C3×C29
HallC2×D13 ⋊ C3×C7×C29
HallC13⋊C3 ⋊ C22×C7×C29

Subgroups

subgroupG/H
center, hypercenterC2×C7×C29D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7×C29
FrattiniC1G
Fitting, socleC2×C7×C13×C29C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C7×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5278

Conjugacy classes & character table

3248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 178);