Finite Group Databasebeta

← Prev (#44539707) Next (#44539709) →

C4×C7×C29×C13⋊C3 #44539708

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C29×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C3×C7×C29)

Splittings

Fitting, HallC4×C7×C13×C29 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C7×C29
HallC7×C13×C29 ⋊ C3×C4
HallC4×C13×C29 ⋊ C3×C7
HallC13×C29 ⋊ C3×C4×C7
HallC4×C7×C13 ⋊ C3×C29
HallC7×C13 ⋊ C3×C4×C29
HallC4×C13 ⋊ C3×C7×C29

Subgroups

subgroupG/H
center, hypercenterC4×C7×C29C13⋊C3
commutator, hypocenterC13C3×C4×C7×C29
FrattiniC2C2×C7×C29×C13⋊C3
FittingC4×C7×C13×C29C3
socleC2×C7×C13×C29C2×C3
prime radicalC2×C7×C29×C13⋊C3C2
cosocleC2×C13C2×C3×C7×C29
LCSG ▷ C13
UCSC1 ◁ C4×C7×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10556

Conjugacy classes & character table

5684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 3);