Finite Group Databasebeta

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C5×C29×C73⋊C3 #44540849

order31755
automorphism?
homologyAbelianization (H1) = C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×C73⋊C3
unambiguous semidirect productC73⋊(C3×C5×C29)
unambiguous semidirect product(C5×C73)⋊(C3×C29)
unambiguous semidirect product(C29×C73)⋊(C3×C5)
unambiguous semidirect product(C5×C29×C73)⋊C3

Splittings

Fitting, socle, HallC5×C29×C73 ⋊ C3
derived, SylowC73 ⋊ C3×C5×C29
HallC29×C73 ⋊ C3×C5
HallC5×C73 ⋊ C3×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29C73⋊C3
commutator, cosocle, hypocenterC73C3×C5×C29
FrattiniC1G
Fitting, socleC5×C29×C73C3
LCSG ▷ C73
UCSC1 ◁ C5×C29

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10585

Conjugacy classes & character table

3915 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31755, 2);