Finite Group Databasebeta

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C2×C32×C5×C71⋊C5 #44544077

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

Aliases

direct productC2×C32×C5×C71⋊C5
unambiguous semidirect product(C2×C71)⋊(C32×C52)
unambiguous semidirect product(C2×C3×C71)⋊(C3×C52)
unambiguous semidirect product(C2×C5×C71)⋊(C32×C5)
unambiguous semidirect product(C2×C32×C71)⋊C52
unambiguous semidirect product(C2×C3×C5×C71)⋊(C3×C5)
unambiguous semidirect product(C2×C32×C5×C71)⋊C5

Splittings

Fitting, socleC2×C32×C5×C71 ⋊ C5
derived, SylowC71 ⋊ C2×C32×C52
HallC2×C32×C71 ⋊ C52
HallC32×C71 ⋊ C2×C52
HallC2×C71 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5C71⋊C5
commutator, cosocle, hypocenterC71C2×C32×C52
FrattiniC1G
Fitting, socleC2×C32×C5×C71C5
LCSG ▷ C71
UCSC1 ◁ C2×C32×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6390

Conjugacy classes & character table

1710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 80);