Finite Group Databasebeta

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C2×C5×C29×D19⋊C3 #45683281

order33060
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C29×D19⋊C3
unambiguous semidirect productD19⋊(C2×C3×C5×C29)
unambiguous semidirect product(C19⋊C3)⋊(C22×C5×C29)
unambiguous semidirect product(C2×D19)⋊(C3×C5×C29)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C5×C29)
unambiguous semidirect product(C2×C5×D19)⋊(C3×C29)
unambiguous semidirect product(C2×C29×D19)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C29×D19)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29D19⋊C3
commutator, cosocle, hypocenterC19C22×C3×C5×C29
FrattiniC1G
Fitting, socleC2×C5×C19×C29C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C5×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5510

Conjugacy classes & character table

2610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 45);