Finite Group Databasebeta

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C2×C5×C29⋊(D19⋊C3) #45683282

order33060
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C29⋊(D19⋊C3)
unambiguous semidirect product(C2×C29)⋊(C5×D19⋊C3)
unambiguous semidirect product(C2×C19⋊C3)⋊(C5×D29)
unambiguous semidirect product(C2×D551)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D551)⋊C3

Splittings

Fitting, socleC2×C5×C19×C29 ⋊ C2×C3
derived, HallC19×C29 ⋊ C22×C3×C5
HallC2×C5×D551 ⋊ C3
HallC5×C29×C19⋊C3 ⋊ C22
HallC5×C19×C29 ⋊ C22×C3
HallC2×D551 ⋊ C3×C5
HallC29×C19⋊C3 ⋊ C22×C5
HallC5×C19⋊C3 ⋊ C2×D29
HallC5×C29 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D29
HallC19⋊C3 ⋊ C2×C5×D29
SylowC29 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C2×C3×C5×D29

Subgroups

subgroupG/H
center, hypercenterC2×C5C29⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C29C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C19×C29C2×C3
LCSG ▷ C19×C29
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5510

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 46);