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C3×C19⋊AGL(1,𝔽11) #20262452

order6270
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C3×D19)
unambiguous semidirect product(C3×D209)⋊C5

Splittings

Fitting, socle, HallC3×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C3×C5
HallC3×C19×C11⋊C5 ⋊ C2
HallC3×D209 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C3
HallD209 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ D19
HallC3×C19 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D19
HallC3×C11 ⋊ C5×D19
SylowC19 ⋊ C3×AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D19

Subgroups

subgroupG/H
center, hypercenterC3C19⋊AGL(1,𝔽11)
commutator, hypocenterC11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C19C2×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D19×AGL(1,𝔽11), D3×C19⋊AGL(1,𝔽11), D57⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D19×AGL(1,𝔽11), D3×C19⋊AGL(1,𝔽11), D57⋊AGL(1,𝔽11), …
maximal quotient ofC3×C19⋊(Dic11⋊C5), C2×C3×C19⋊AGL(1,𝔽11), C9×C19⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6270, 22);