Finite Group Databasebeta

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D5×C29⋊(D19⋊C3) #45683277

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

Aliases

direct productD5×C29⋊(D19⋊C3)
unambiguous semidirect product(D5×C29)⋊(D19⋊C3)
unambiguous semidirect product(D5×C19⋊C3)⋊D29
unambiguous semidirect product(D5×D551)⋊C3

Splittings

Fitting, socle, derived, HallC5×C19×C29 ⋊ C22×C3
HallD5×D551 ⋊ 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 ⋊ D5×D29
SylowC29 ⋊ D5×D19⋊C3
SylowC19 ⋊ C3×D5×D29
SylowC5 ⋊ C2×C29⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C29C22×C3
LCSG ▷ C5×C19×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2755

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 41);