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C19×AGL(1,𝔽11) #14523459

order2090
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C19)
unambiguous semidirect product(C11⋊C5)⋊(C2×C19)
unambiguous semidirect product(C19×D11)⋊C5

Splittings

Fitting, socle, HallC11×C19 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C19
HallC19×C11⋊C5 ⋊ C2
HallC19×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C19
HallD11 ⋊ C5×C19

Subgroups

subgroupG/H
center, hypercenterC19AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C5×C19
FrattiniC1G
Fitting, socleC11×C19C2×C5
LCSG ▷ C11
UCSC1 ◁ C19

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 209

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25,26,24,29,22,23,30,27,28);(20,21,24,29,23,26,30,25,28,27,22)

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×AGL(1,𝔽11), C2×C19×AGL(1,𝔽11), C7×C19×AGL(1,𝔽11), …
maximal normal subgroup ofD19×AGL(1,𝔽11), C2×C19×AGL(1,𝔽11), C7×C19×AGL(1,𝔽11), …
maximal quotient ofC19×Dic11⋊C5, C2×C19×AGL(1,𝔽11), C7×C19×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2090, 11);