Finite Group Databasebeta

← Prev (#34037884) Next (#34037886) →

C5×C3⋊(C11⋊(D19⋊C3)) #34037885

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

Aliases

direct productC5×C3⋊(C11⋊(D19⋊C3))
unambiguous semidirect productC3⋊(C5×C11⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C5×D33)
unambiguous semidirect product(C5×D627)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C3
derivedC3×C11×C19 ⋊ C2×C3×C5
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC5×C11×C19 ⋊ C3×D3
HallC3×C5×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C3×C5×D3
HallC3×C19⋊C3 ⋊ C5×D11
HallC5×C19 ⋊ C3×D33
HallC5×C11 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C3×C5×D33
SylowC11 ⋊ C5×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C11⋊(D19⋊C3))
commutator, cosocle, hypocenterC3×C11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C3
LCSG ▷ C3×C11×C19
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D33×D19⋊C3, C5×D11×C3⋊(D19⋊C3), C5×D3×C11⋊(D19⋊C3), …
maximal normal subgroup ofC5×D33×D19⋊C3, C5×D11×C3⋊(D19⋊C3), C5×D3×C11⋊(D19⋊C3), …
maximal quotient ofC5×C3⋊(C11⋊((C19⋊C3)⋊C4)), C2×C5×C3⋊(C11⋊(D19⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 78);