Finite Group Databasebeta

← Prev (#44565708) Next (#44565710) →

C2×C5×C29×C37⋊C3 #44565709

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

Aliases

direct productC2×C5×C29×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C3×C5×C29)
unambiguous semidirect product(C2×C5×C37)⋊(C3×C29)
unambiguous semidirect product(C2×C29×C37)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C29×C37)⋊C3

Splittings

Fitting, socle, HallC2×C5×C29×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C5×C29
HallC5×C29×C37 ⋊ C2×C3
HallC2×C29×C37 ⋊ C3×C5
HallC29×C37 ⋊ C2×C3×C5
HallC2×C5×C37 ⋊ C3×C29
HallC5×C37 ⋊ C2×C3×C29
HallC2×C37 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29C37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C5×C29
FrattiniC1G
Fitting, socleC2×C5×C29×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10730

Conjugacy classes & character table

4350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32190, 2);