Finite Group Databasebeta

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D5×C29×D19⋊C3 #45683275

order33060
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productD5×C29×D19⋊C3
unambiguous semidirect productD19⋊(C3×D5×C29)
unambiguous semidirect product(D5×D19)⋊(C3×C29)
unambiguous semidirect product(C5×D19⋊C3)⋊(C2×C29)
unambiguous semidirect product(D5×C19⋊C3)⋊(C2×C29)
unambiguous semidirect product(C5⋊(D19⋊C3))⋊(C2×C29)
unambiguous semidirect product(D5×C29×D19)⋊C3

Splittings

Fitting, socle, HallC5×C19×C29 ⋊ C22×C3
derived, HallC5×C19 ⋊ C22×C3×C29
HallD5×C29×D19 ⋊ C3
HallC5×C29×C19⋊C3 ⋊ C22
HallC29×C19⋊C3 ⋊ C2×D5
HallC19×C29 ⋊ C2×C3×D5
HallD5×D19 ⋊ C3×C29
HallC5×C19⋊C3 ⋊ C22×C29
HallC5×C29 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×D5×C29
SylowC19 ⋊ C2×C3×D5×C29
SylowC5 ⋊ C2×C29×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC29D5×D19⋊C3
commutator, cosocle, hypocenterC5×C19C22×C3×C29
FrattiniC1G
Fitting, socleC5×C19×C29C22×C3
LCSG ▷ C5×C19
UCSC1 ◁ C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2755

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 39);