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C7×C19⋊AGL(1,𝔽11) #28410704

order14630
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19⋊AGL(1,𝔽11)
unambiguous semidirect productC19⋊(C7×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D19)
unambiguous semidirect productD209⋊(C5×C7)
unambiguous semidirect product(C7×D209)⋊C5

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C5×C7
HallC7×C19×C11⋊C5 ⋊ C2
HallC7×D209 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C7
HallD209 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ D19
HallC7×C19 ⋊ AGL(1,𝔽11)
HallC7×C11 ⋊ C5×D19
HallC11⋊C5 ⋊ C7×D19
SylowC19 ⋊ C7×AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D19

Subgroups

subgroupG/H
center, hypercenterC7C19⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C19C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C19C2×C5
LCSG ▷ C11×C19
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D19×AGL(1,𝔽11), D7×C19⋊AGL(1,𝔽11), D133⋊AGL(1,𝔽11), …
maximal normal subgroup ofC7×D19×AGL(1,𝔽11), D7×C19⋊AGL(1,𝔽11), D133⋊AGL(1,𝔽11), …
maximal quotient ofC7×C19⋊(Dic11⋊C5), C2×C7×C19⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14630, 20);