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C13×AGL(1,𝔽11) #13083641

order1430
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C13)
unambiguous semidirect product(C11⋊C5)⋊(C2×C13)
unambiguous semidirect product(C13×D11)⋊C5

Splittings

Fitting, socle, HallC11×C13 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C13
HallC13×C11⋊C5 ⋊ C2
HallC13×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C13
HallD11 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC13AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C5×C13
FrattiniC1G
Fitting, socleC11×C13C2×C5
LCSG ▷ C11
UCSC1 ◁ C13

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 143

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×AGL(1,𝔽11), C2×C13×AGL(1,𝔽11), C3×C13×AGL(1,𝔽11), …
maximal normal subgroup ofD13×AGL(1,𝔽11), C2×C13×AGL(1,𝔽11), C3×C13×AGL(1,𝔽11), …
maximal quotient ofC13×Dic11⋊C5, C2×C13×AGL(1,𝔽11), C3×C13×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1430, 2);