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C3×C17×AGL(1,𝔽11) #19150508

order5610
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C17)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C17)
unambiguous semidirect product(C3×D11)⋊(C5×C17)
unambiguous semidirect product(C17×D11)⋊(C3×C5)
unambiguous semidirect product(C3×C17×D11)⋊C5

Splittings

Fitting, socle, HallC3×C11×C17 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C17
HallC3×C17×C11⋊C5 ⋊ C2
HallC3×C17×D11 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×C3
HallC17×D11 ⋊ C3×C5
HallC11×C17 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C17
HallC3×D11 ⋊ C5×C17
HallC11⋊C5 ⋊ C2×C3×C17
HallC3×C11 ⋊ C2×C5×C17
HallD11 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17AGL(1,𝔽11)
commutator, hypocenterC11C2×C3×C5×C17
FrattiniC1G
Fitting, socleC3×C11×C17C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D17×AGL(1,𝔽11), D3×C17×AGL(1,𝔽11), D51×AGL(1,𝔽11), …
maximal normal subgroup ofC3×D17×AGL(1,𝔽11), D3×C17×AGL(1,𝔽11), D51×AGL(1,𝔽11), …
maximal quotient ofC3×C17×Dic11⋊C5, C2×C3×C17×AGL(1,𝔽11), C9×C17×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5610, 19);