Finite Group Databasebeta

← Prev (#44565728) Next (#44565730) →

C29×C5⋊(D37⋊C3) #44565729

order32190
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×C5⋊(D37⋊C3)
unambiguous semidirect productC5⋊(C29×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(D5×C29)
unambiguous semidirect productD185⋊(C3×C29)
unambiguous semidirect product(C29×D185)⋊C3

Splittings

Fitting, socle, HallC5×C29×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C2×C3×C29
HallC5×C29×C37⋊C3 ⋊ C2
HallC29×D185 ⋊ C3
HallC29×C37⋊C3 ⋊ D5
HallC29×C37 ⋊ C3×D5
HallC5×C37⋊C3 ⋊ C2×C29
HallD185 ⋊ C3×C29
HallC5×C29 ⋊ D37⋊C3
HallC37⋊C3 ⋊ D5×C29
SylowC37 ⋊ C3×D5×C29
SylowC5 ⋊ C29×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC29C5⋊(D37⋊C3)
commutator, cosocle, hypocenterC5×C37C2×C3×C29
FrattiniC1G
Fitting, socleC5×C29×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5365

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 22);