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C11⋊C5×D159 #31775827

order17490
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D159
unambiguous semidirect productC3⋊(C11⋊C5×D53)
unambiguous semidirect productC53⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D159)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C53 ⋊ C2×C5
HallC3×C53×C11⋊C5 ⋊ C2
HallC11×D159 ⋊ C5
HallC53×C11⋊C5 ⋊ D3
HallC11×C53 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D53
HallC3×C53 ⋊ C2×C11⋊C5
SylowC53 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D53
SylowC11 ⋊ C5×D159
SylowC3 ⋊ C11⋊C5×D53

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C53C2×C5
LCSG ▷ C3×C11×C53
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1749

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×D159, D159⋊AGL(1,𝔽11), D3×C11⋊C5×D53, …
maximal normal subgroup ofAGL(1,𝔽11)×D159, D159⋊AGL(1,𝔽11), D3×C11⋊C5×D53, …
maximal quotient ofC11⋊C5×Dic159, C2×C11⋊C5×D159

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 22);