Finite Group Databasebeta

← Prev (#44531148) Next (#44531150) →

C7×C9×C71⋊C7 #44531149

order31311
automorphism?
homologyAbelianization (H1) = C72×C9 · Schur multiplier (H2) = C7

Aliases

direct productC7×C9×C71⋊C7
unambiguous semidirect productC71⋊(C72×C9)
unambiguous semidirect product(C9×C71)⋊C72
unambiguous semidirect product(C7×C9×C71)⋊C7

Splittings

FittingC7×C9×C71 ⋊ C7
derived, SylowC71 ⋊ C72×C9
HallC9×C71 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC7×C9C71⋊C7
commutator, hypocenterC71C72×C9
FrattiniC3C3×C7×C71⋊C7
FittingC7×C9×C71C7
socleC3×C7×C71C3×C7
prime radicalC3×C7×C71⋊C7C3
cosocleC3×C71C3×C72
LCSG ▷ C71
UCSC1 ◁ C7×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4473

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31311, 9);