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C3×C29×C71⋊C5 #44525297

order30885
automorphism?
homologyAbelianization (H1) = C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×C71⋊C5
unambiguous semidirect productC71⋊(C3×C5×C29)
unambiguous semidirect product(C3×C71)⋊(C5×C29)
unambiguous semidirect product(C29×C71)⋊(C3×C5)
unambiguous semidirect product(C3×C29×C71)⋊C5

Splittings

Fitting, socle, HallC3×C29×C71 ⋊ C5
derived, SylowC71 ⋊ C3×C5×C29
HallC29×C71 ⋊ C3×C5
HallC3×C71 ⋊ C5×C29

Subgroups

subgroupG/H
center, hypercenterC3×C29C71⋊C5
commutator, cosocle, hypocenterC71C3×C5×C29
FrattiniC1G
Fitting, socleC3×C29×C71C5
LCSG ▷ C71
UCSC1 ◁ C3×C29

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6177

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30885, 2);