Finite Group Databasebeta

← Prev (#44565729) Next (#44565731) →

C37⋊C3×D145 #44565730

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

Aliases

direct productC37⋊C3×D145
unambiguous semidirect productC5⋊(D29×C37⋊C3)
unambiguous semidirect productC29⋊(D5×C37⋊C3)
unambiguous semidirect product(C37×D145)⋊C3

Splittings

Fitting, socle, derived, HallC5×C29×C37 ⋊ C2×C3
HallC5×C29×C37⋊C3 ⋊ C2
HallC37×D145 ⋊ C3
HallC29×C37⋊C3 ⋊ D5
HallC29×C37 ⋊ C3×D5
HallC5×C37⋊C3 ⋊ D29
HallC5×C37 ⋊ C3×D29
HallC5×C29 ⋊ C2×C37⋊C3
SylowC37 ⋊ C3×D145
SylowC29 ⋊ D5×C37⋊C3
SylowC5 ⋊ D29×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C29×C37C2×C3
LCSG ▷ C5×C29×C37
UCSC1

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, 23);