Finite Group Databasebeta

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C2×C5⋊(C29⋊(D19⋊C3)) #45683285

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

Aliases

direct productC2×C5⋊(C29⋊(D19⋊C3))
unambiguous semidirect product(C2×C5)⋊(C29⋊(D19⋊C3))
unambiguous semidirect product(C2×C29)⋊(C5⋊(D19⋊C3))
unambiguous semidirect product(C2×C19⋊C3)⋊D145
unambiguous semidirect product(C2×D2755)⋊C3

Splittings

Fitting, socleC2×C5×C19×C29 ⋊ C2×C3
derived, HallC5×C19×C29 ⋊ C22×C3
HallC2×D2755 ⋊ C3
HallC5×C29×C19⋊C3 ⋊ C22
HallC29×C19⋊C3 ⋊ C2×D5
HallC19×C29 ⋊ C2×C3×D5
HallC5×C19⋊C3 ⋊ C2×D29
HallC5×C29 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D29
HallC19⋊C3 ⋊ C2×D145
SylowC29 ⋊ C2×C5⋊(D19⋊C3)
SylowC19 ⋊ C2×C3×D145
SylowC5 ⋊ C2×C29⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C29⋊(D19⋊C3))
commutator, cosocle, hypocenterC5×C19×C29C22×C3
FrattiniC1G
Fitting, socleC2×C5×C19×C29C2×C3
LCSG ▷ C5×C19×C29
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5510

Conjugacy classes & character table

1314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 49);