Finite Group Databasebeta

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C3×D5×D551 #45683305

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

Aliases

direct productC3×D5×D551
unambiguous semidirect product(D5×C29)⋊(C3×D19)

Splittings

Fitting, socle, HallC3×C5×C19×C29 ⋊ C22
derived, HallC5×C19×C29 ⋊ C22×C3
HallC3×C19×C29 ⋊ C2×D5
HallC19×C29 ⋊ C2×C3×D5
HallC3×C5×C29 ⋊ C2×D19
HallC3×C5×C19 ⋊ C2×D29
HallC5×C29 ⋊ C2×C3×D19
HallC5×C19 ⋊ C2×C3×D29
HallC3×C29 ⋊ D5×D19
HallC3×C19 ⋊ D5×D29
SylowC29 ⋊ C3×D5×D19
SylowC19 ⋊ C3×D5×D29
HallC3×C5 ⋊ C2×D551
SylowC5 ⋊ C2×C3×D551

Subgroups

subgroupG/H
center, hypercenterC3D5×D551
commutator, cosocle, hypocenterC5×C19×C29C22×C3
FrattiniC1G
Fitting, socleC3×C5×C19×C29C22
LCSG ▷ C5×C19×C29
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8265

Conjugacy classes & character table

3324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 69);