Finite Group Databasebeta

← Prev (#44544054) Next (#44544056) →

C32×C5×D71⋊C5 #44544055

order31950
automorphism?
homologyAbelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC32×C5×D71⋊C5
unambiguous semidirect productD71⋊(C32×C52)
unambiguous semidirect product(C71⋊C5)⋊(C2×C32×C5)
unambiguous semidirect product(C3×D71)⋊(C3×C52)
unambiguous semidirect product(C5×D71)⋊(C32×C5)
unambiguous semidirect product(C32×D71)⋊C52
unambiguous semidirect product(C3×C5×D71)⋊(C3×C5)
unambiguous semidirect product(C32×C5×D71)⋊C5

Splittings

Fitting, socleC32×C5×C71 ⋊ C2×C5
derived, SylowC71 ⋊ C2×C32×C52
HallC32×C5×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ C2×C32
HallC32×D71 ⋊ C52
HallC32×C71 ⋊ C2×C52
HallD71 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC32×C5D71⋊C5
commutator, cosocle, hypocenterC71C2×C32×C52
FrattiniC1G
Fitting, socleC32×C5×C71C2×C5
LCSG ▷ C71
UCSC1 ◁ C32×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 58);