Finite Group Databasebeta

← Prev (#32915751) Next (#32915753) →

AGL(1,𝔽11)×C169 #32915752

order18590
automorphism?
homologyAbelianization (H1) = C2×C5×C169 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×C169
unambiguous semidirect productD11⋊(C5×C169)
unambiguous semidirect product(C11⋊C5)⋊(C2×C169)
unambiguous semidirect product(D11×C169)⋊C5

Splittings

Fitting, HallC11×C169 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C169
HallC11⋊C5×C169 ⋊ C2
HallD11×C169 ⋊ C5
HallC11⋊C5 ⋊ C2×C169
HallD11 ⋊ C5×C169

Subgroups

subgroupG/H
center, hypercenterC169AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C169
FrattiniC13C13×AGL(1,𝔽11)
FittingC11×C169C2×C5
socle, cosocleC11×C13C2×C5×C13
prime radicalC13×AGL(1,𝔽11)C13
LCSG ▷ C11
UCSC1 ◁ C169

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1859

Conjugacy classes & character table

1859 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D169, C2×AGL(1,𝔽11)×C169
maximal normal subgroup ofAGL(1,𝔽11)×D169, C2×AGL(1,𝔽11)×C169
maximal quotient ofC169×Dic11⋊C5, C2×AGL(1,𝔽11)×C169

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18590, 3);