Finite Group Databasebeta

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C3×C3⋊(C5⋊(D71⋊C5)) #44544060

order31950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(C5⋊(D71⋊C5))
unambiguous semidirect productC3⋊(C3×C5⋊(D71⋊C5))
unambiguous semidirect productC5⋊(C3×C3⋊(D71⋊C5))
unambiguous semidirect product(C71⋊C5)⋊(C3×D15)
unambiguous semidirect productD1065⋊(C3×C5)
unambiguous semidirect product(C3×D1065)⋊C5

Splittings

Fitting, socleC32×C5×C71 ⋊ C2×C5
derivedC3×C5×C71 ⋊ C2×C3×C5
HallC32×C5×C71⋊C5 ⋊ C2
HallC5×C71⋊C5 ⋊ C3×D3
HallC32×C71 ⋊ C5×D5
SylowC71 ⋊ C3×C5×D15
SylowC32 ⋊ C5⋊(D71⋊C5)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C5⋊(D71⋊C5))
commutator, cosocle, hypocenterC3×C5×C71C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C71C2×C5
LCSG ▷ C3×C5×C71
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2130

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 63);