Finite Group Databasebeta

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C5×C29⋊(D37⋊C3) #44565727

order32190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29⋊(D37⋊C3)
unambiguous semidirect productC29⋊(C5×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(C5×D29)
unambiguous semidirect productD1073⋊(C3×C5)
unambiguous semidirect product(C5×D1073)⋊C3

Splittings

Fitting, socle, HallC5×C29×C37 ⋊ C2×C3
derived, HallC29×C37 ⋊ C2×C3×C5
HallC5×C29×C37⋊C3 ⋊ C2
HallC5×D1073 ⋊ C3
HallC29×C37⋊C3 ⋊ C2×C5
HallD1073 ⋊ C3×C5
HallC5×C37⋊C3 ⋊ D29
HallC5×C37 ⋊ C3×D29
HallC5×C29 ⋊ D37⋊C3
HallC37⋊C3 ⋊ C5×D29
SylowC37 ⋊ C3×C5×D29
SylowC29 ⋊ C5×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C29⋊(D37⋊C3)
commutator, cosocle, hypocenterC29×C37C2×C3×C5
FrattiniC1G
Fitting, socleC5×C29×C37C2×C3
LCSG ▷ C29×C37
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5365

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 20);