Finite Group Databasebeta

← Prev (#44568151) Next (#44568153) →

C13×(C71⋊C5)⋊C7 #44568152

order32305
automorphism?
homologyAbelianization (H1) = C5×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C71⋊C5)⋊C7
unambiguous semidirect product(C71⋊C5)⋊(C7×C13)
unambiguous semidirect product(C71⋊C7)⋊(C5×C13)
unambiguous semidirect product(C13×C71⋊C5)⋊C7
unambiguous semidirect product(C13×C71⋊C7)⋊C5

Splittings

Fitting, socle, HallC13×C71 ⋊ C5×C7
derived, SylowC71 ⋊ C5×C7×C13
HallC13×C71⋊C7 ⋊ C5
HallC13×C71⋊C5 ⋊ C7
HallC71⋊C7 ⋊ C5×C13
HallC71⋊C5 ⋊ C7×C13

Subgroups

subgroupG/H
center, hypercenterC13(C71⋊C5)⋊C7
commutator, cosocle, hypocenterC71C5×C7×C13
FrattiniC1G
Fitting, socleC13×C71C5×C7
LCSG ▷ C71
UCSC1 ◁ C13

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 923

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32305, 4);