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AGL(1,𝔽11)×C137 #28418957

order15070
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C137 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×C137
unambiguous semidirect productD11⋊(C5×C137)
unambiguous semidirect product(C11⋊C5)⋊(C2×C137)
unambiguous semidirect product(D11×C137)⋊C5

Splittings

Fitting, socle, HallC11×C137 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C137
HallC11⋊C5×C137 ⋊ C2
HallD11×C137 ⋊ C5
HallC11⋊C5 ⋊ C2×C137
HallD11 ⋊ C5×C137

Subgroups

subgroupG/H
center, hypercenterC137AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C5×C137
FrattiniC1G
Fitting, socleC11×C137C2×C5
LCSG ▷ C11
UCSC1 ◁ C137

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1507

Conjugacy classes & character table

1507 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D137, C2×AGL(1,𝔽11)×C137
maximal normal subgroup ofAGL(1,𝔽11)×D137, C2×AGL(1,𝔽11)×C137
maximal quotient ofC137×Dic11⋊C5, C2×AGL(1,𝔽11)×C137

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15070, 11);