Finite Group Databasebeta

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C3×C37×D145 #44565715

order32190
automorphism?
homologyAbelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C37×D145
unambiguous semidirect productC5⋊(C3×C37×D29)
unambiguous semidirect productC29⋊(C3×D5×C37)

Splittings

Fitting, socle, HallC3×C5×C29×C37 ⋊ C2
derived, HallC5×C29 ⋊ C2×C3×C37
HallC5×C29×C37 ⋊ C2×C3
HallC3×C29×C37 ⋊ D5
HallC29×C37 ⋊ C3×D5
HallC3×C5×C37 ⋊ D29
HallC3×C5×C29 ⋊ C2×C37
HallC5×C37 ⋊ C3×D29
HallC3×C29 ⋊ D5×C37
SylowC29 ⋊ C3×D5×C37
HallC3×C5 ⋊ C37×D29
SylowC5 ⋊ C3×C37×D29

Subgroups

subgroupG/H
center, hypercenterC3×C37D145
commutator, cosocle, hypocenterC5×C29C2×C3×C37
FrattiniC1G
Fitting, socleC3×C5×C29×C37C2
LCSG ▷ C5×C29
UCSC1 ◁ C3×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16095

Conjugacy classes & character table

8214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 8);