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C13⋊AGL(1,𝔽11) #13083642

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

Aliases

unambiguous semidirect productC13⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊D13
unambiguous semidirect productD143⋊C5

Splittings

Fitting, socle, derived, HallC11×C13 ⋊ C2×C5
HallC13×C11⋊C5 ⋊ C2
HallD143 ⋊ C5
HallC11⋊C5 ⋊ D13
SylowC13 ⋊ AGL(1,𝔽11)
SylowC11 ⋊ C5×D13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C13C2×C5
LCSG ▷ C11×C13
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,5,11,13|c^a=c^10,d^a=d^12,c^b=c^4

Conjugacy classes & character table

53 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 of(C11⋊C5)⋊Dic13, C2×C13⋊AGL(1,𝔽11), C3×C13⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1430, 3);