Finite Group Databasebeta

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C32×D5×C71⋊C5 #44544057

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

Aliases

direct productC32×D5×C71⋊C5
unambiguous semidirect productC5⋊(C2×C32×C71⋊C5)
unambiguous semidirect product(D5×C71)⋊(C32×C5)
unambiguous semidirect product(C3×D5×C71)⋊(C3×C5)
unambiguous semidirect product(C32×D5×C71)⋊C5

Splittings

Fitting, socleC32×C5×C71 ⋊ C2×C5
derivedC5×C71 ⋊ C2×C32×C5
HallC32×C5×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ C2×C32
HallC32×C71 ⋊ C5×D5
SylowC71 ⋊ C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC32D5×C71⋊C5
commutator, cosocle, hypocenterC5×C71C2×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C71C2×C5
LCSG ▷ C5×C71
UCSC1 ◁ C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 60);