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AGL(1,𝔽11)×C49⋊C3 #30633489

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×C49⋊C3
unambiguous semidirect productD11⋊(C5×C49⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C2×C49⋊C3)
unambiguous semidirect product(D11×C49⋊C3)⋊C5
unambiguous semidirect product(C49×AGL(1,𝔽11))⋊C3

Splittings

Fitting, derived, HallC11×C49 ⋊ C2×C3×C5
HallC11⋊C5×C49⋊C3 ⋊ C2
HallC49×AGL(1,𝔽11) ⋊ C3
HallD11×C49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×C3
HallC11×C49⋊C3 ⋊ C2×C5
HallD11×C49 ⋊ C3×C5
HallC11⋊C5 ⋊ C2×C49⋊C3
SylowC49 ⋊ C3×AGL(1,𝔽11)
HallD11 ⋊ C5×C49⋊C3
SylowC11 ⋊ C2×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7ΓL(1,𝔽8)×AGL(1,𝔽11)
socleC7×C11C2×C5×ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 539

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D49⋊C3, C2×AGL(1,𝔽11)×C49⋊C3
maximal normal subgroup ofAGL(1,𝔽11)×D49⋊C3, C2×AGL(1,𝔽11)×C49⋊C3
maximal quotient ofC49⋊C3×Dic11⋊C5, C2×AGL(1,𝔽11)×C49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 34);