Finite Group Databasebeta

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C3×C5×C19×D33 #34037906

order18810
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C19×D33
unambiguous semidirect productC3⋊(C3×C5×C19×D11)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C2
derivedC3×C11 ⋊ C2×C3×C5×C19
HallC32×C11×C19 ⋊ C2×C5
HallC5×C11×C19 ⋊ C3×D3
HallC32×C5×C19 ⋊ D11
HallC32×C5×C11 ⋊ C2×C19
HallC11×C19 ⋊ C3×C5×D3
HallC32×C19 ⋊ C5×D11
HallC32×C11 ⋊ C2×C5×C19
HallC5×C11 ⋊ C3×D3×C19
HallC32×C5 ⋊ C19×D11
SylowC11 ⋊ C3×C5×D3×C19
SylowC32 ⋊ C5×C19×D11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C19D33
commutator, cosocle, hypocenterC3×C11C2×C3×C5×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C2
LCSG ▷ C3×C11
UCSC1 ◁ C3×C5×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

5130 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D19×D33, C3×C5×D3×C19×D11, C3×C5×D33⋊D19, …
maximal normal subgroup ofC3×C5×D19×D33, C3×C5×D3×C19×D11, C3×C5×D33⋊D19, …
maximal quotient ofC3×C5×C19×Dic33, C2×C3×C5×C19×D33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 99);