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AGL(1,𝔽11)×C289 #44541099

order31790
automorphism?
homologyAbelianization (H1) = C2×C5×C289 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×C289
unambiguous semidirect productD11⋊(C5×C289)
unambiguous semidirect product(C11⋊C5)⋊(C2×C289)
unambiguous semidirect product(D11×C289)⋊C5

Splittings

Fitting, HallC11×C289 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C289
HallC11⋊C5×C289 ⋊ C2
HallD11×C289 ⋊ C5
HallC11⋊C5 ⋊ C2×C289
HallD11 ⋊ C5×C289

Subgroups

subgroupG/H
center, hypercenterC289AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C289
FrattiniC17C17×AGL(1,𝔽11)
FittingC11×C289C2×C5
socle, cosocleC11×C17C2×C5×C17
prime radicalC17×AGL(1,𝔽11)C17
LCSG ▷ C11
UCSC1 ◁ C289

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3179

Conjugacy classes & character table

3179 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31790, 3);