Finite Group Databasebeta

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C5×C11×D159 #31775816

order17490
isoclinismisoclinic class of D159
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D159
unambiguous semidirect productC3⋊(C5×C11×D53)
unambiguous semidirect productC53⋊(C5×D3×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC3×C53 ⋊ C2×C5×C11
HallC5×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ C2×C5
HallC3×C5×C53 ⋊ C2×C11
HallC11×C53 ⋊ C5×D3
HallC5×C53 ⋊ D3×C11
HallC3×C5×C11 ⋊ D53
SylowC53 ⋊ C5×D3×C11
HallC3×C11 ⋊ C5×D53
HallC3×C5 ⋊ C11×D53
SylowC3 ⋊ C5×C11×D53

Subgroups

subgroupG/H
center, hypercenterC5×C11D159
commutator, cosocle, hypocenterC3×C53C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3×C53
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4455 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D53, C5×D11×D159, C5×D33⋊D53, …
maximal normal subgroup ofC5×D3×C11×D53, C5×D11×D159, C5×D33⋊D53, …
maximal quotient ofC5×C11×Dic159, C2×C5×C11×D159

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 11);