Finite Group Databasebeta

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C5×C29×D37⋊C3 #44565725

order32190
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×D37⋊C3
unambiguous semidirect productD37⋊(C3×C5×C29)
unambiguous semidirect product(C37⋊C3)⋊(C2×C5×C29)
unambiguous semidirect product(C5×D37)⋊(C3×C29)
unambiguous semidirect product(C29×D37)⋊(C3×C5)
unambiguous semidirect product(C5×C29×D37)⋊C3

Splittings

Fitting, socle, HallC5×C29×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C3×C5×C29
HallC5×C29×C37⋊C3 ⋊ C2
HallC5×C29×D37 ⋊ C3
HallC29×C37⋊C3 ⋊ C2×C5
HallC29×D37 ⋊ C3×C5
HallC29×C37 ⋊ C2×C3×C5
HallC5×C37⋊C3 ⋊ C2×C29
HallC5×D37 ⋊ C3×C29
HallC5×C37 ⋊ C2×C3×C29
HallC37⋊C3 ⋊ C2×C5×C29
HallD37 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29D37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C5×C29
FrattiniC1G
Fitting, socleC5×C29×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5365

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 18);