Finite Group Databasebeta

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C32×C17×C41⋊C5 #44535853

order31365
automorphism?
homologyAbelianization (H1) = C32×C5×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C17×C41⋊C5
unambiguous semidirect productC41⋊(C32×C5×C17)
unambiguous semidirect product(C3×C41)⋊(C3×C5×C17)
unambiguous semidirect product(C32×C41)⋊(C5×C17)
unambiguous semidirect product(C17×C41)⋊(C32×C5)
unambiguous semidirect product(C3×C17×C41)⋊(C3×C5)
unambiguous semidirect product(C32×C17×C41)⋊C5

Splittings

Fitting, socle, HallC32×C17×C41 ⋊ C5
derived, SylowC41 ⋊ C32×C5×C17
HallC17×C41 ⋊ C32×C5
HallC32×C41 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC32×C17C41⋊C5
commutator, cosocle, hypocenterC41C32×C5×C17
FrattiniC1G
Fitting, socleC32×C17×C41C5
LCSG ▷ C41
UCSC1 ◁ C32×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6273

Conjugacy classes & character table

1989 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31365, 4);