Finite Group Databasebeta

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C37×D435 #44565723

order32190
automorphism?
homologyAbelianization (H1) = C2×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×D435
unambiguous semidirect productC3⋊(C37×D145)
unambiguous semidirect productC5⋊(C37×D87)
unambiguous semidirect productC29⋊(D15×C37)

Splittings

Fitting, socle, HallC3×C5×C29×C37 ⋊ C2
derived, HallC3×C5×C29 ⋊ C2×C37
HallC5×C29×C37 ⋊ D3
HallC3×C29×C37 ⋊ D5
HallC29×C37 ⋊ D15
HallC3×C5×C37 ⋊ D29
HallC5×C37 ⋊ D87
HallC5×C29 ⋊ D3×C37
HallC3×C37 ⋊ D145
HallC3×C29 ⋊ D5×C37
SylowC29 ⋊ D15×C37
HallC3×C5 ⋊ C37×D29
SylowC5 ⋊ C37×D87
SylowC3 ⋊ C37×D145

Subgroups

subgroupG/H
center, hypercenterC37D435
commutator, cosocle, hypocenterC3×C5×C29C2×C37
FrattiniC1G
Fitting, socleC3×C5×C29×C37C2
LCSG ▷ C3×C5×C29
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16095

Conjugacy classes & character table

8103 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 16);