Finite Group Databasebeta

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C2×C5×C9×C71⋊C5 #44544041

order31950
automorphism?
homologyAbelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×C9×C71⋊C5
unambiguous semidirect product(C2×C71)⋊(C52×C9)
unambiguous semidirect product(C2×C5×C71)⋊(C5×C9)
unambiguous semidirect product(C2×C9×C71)⋊C52
unambiguous semidirect product(C2×C5×C9×C71)⋊C5

Splittings

FittingC2×C5×C9×C71 ⋊ C5
derived, SylowC71 ⋊ C2×C52×C9
HallC2×C9×C71 ⋊ C52
HallC9×C71 ⋊ C2×C52
HallC2×C71 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9C71⋊C5
commutator, hypocenterC71C2×C52×C9
FrattiniC3C2×C3×C5×C71⋊C5
FittingC2×C5×C9×C71C5
socleC2×C3×C5×C71C3×C5
prime radicalC2×C3×C5×C71⋊C5C3
cosocleC3×C71C2×C3×C52
LCSG ▷ C71
UCSC1 ◁ C2×C5×C9

96 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, 44);