Finite Group Databasebeta

← Prev (#44539797) Next (#44539799) →

C22×C13⋊C3×C29⋊C7 #44539798

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

Aliases

direct productC22×C13⋊C3×C29⋊C7
unambiguous semidirect product(C22×C29×C13⋊C3)⋊C7

Splittings

Fitting, socle, HallC22×C13×C29 ⋊ C3×C7
derived, HallC13×C29 ⋊ C22×C3×C7
HallC22×C13×C29⋊C7 ⋊ C3
HallC22×C29×C13⋊C3 ⋊ C7
HallC13×C29⋊C7 ⋊ C22×C3
HallC29×C13⋊C3 ⋊ C22×C7
HallC22×C29 ⋊ C7×C13⋊C3
HallC22×C13 ⋊ C3×C29⋊C7
SylowC29 ⋊ C22×C7×C13⋊C3
SylowC13 ⋊ C22×C3×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC22C13⋊C3×C29⋊C7
commutator, cosocle, hypocenterC13×C29C22×C3×C7
FrattiniC1G
Fitting, socleC22×C13×C29C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C22

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1508

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 93);