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(C13⋊C3)⋊AGL(1,𝔽11) #16864271

order4290
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C13⋊C3)⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(D13⋊C3)
unambiguous semidirect product(C11⋊(D13⋊C3))⋊C5
unambiguous semidirect product(C13⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socle, derived, HallC11×C13 ⋊ C2×C3×C5
HallC13⋊C3×C11⋊C5 ⋊ C2
HallC13⋊AGL(1,𝔽11) ⋊ C3
HallC11⋊(D13⋊C3) ⋊ C5
HallC13×C11⋊C5 ⋊ C2×C3
HallC11×C13⋊C3 ⋊ C2×C5
HallD143 ⋊ C3×C5
HallC11⋊C5 ⋊ D13⋊C3
HallC13⋊C3 ⋊ AGL(1,𝔽11)
SylowC13 ⋊ C3×AGL(1,𝔽11)
SylowC11 ⋊ C5×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,3,5,11,13|d^a=d^10,e^a=e^12,e^b=e^3,d^c=d^4

Conjugacy classes & character table

47 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C13⋊C3)⋊AGL(1,𝔽11), C3⋊((C13⋊C3)⋊AGL(1,𝔽11)), C5×(C13⋊C3)⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×(C13⋊C3)⋊AGL(1,𝔽11), C5×(C13⋊C3)⋊AGL(1,𝔽11), C7×(C13⋊C3)⋊AGL(1,𝔽11)
maximal quotient of(C11⋊C5)⋊(D13⋊C9), C3×(C13⋊C3)⋊AGL(1,𝔽11), C3⋊((C13⋊C3)⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 36);