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C11×ΓL(1,𝔽8)⋊(D13⋊C3) #31825005

order18018
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×ΓL(1,𝔽8)⋊(D13⋊C3)
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C11×AGL(1,𝔽7))
unambiguous semidirect product((C13⋊C3)⋊D7)⋊(C3×C11)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D13)⋊(C3×C11)
unambiguous semidirect product#10587722⋊(C3×C11)
unambiguous semidirect product#10587723⋊(C3×C11)
unambiguous semidirect product(C11×(C13⋊C3)⋊D7)⋊C3
unambiguous semidirect product(C11×ΓL(1,𝔽8)⋊D13)⋊C3
unambiguous semidirect product(C11×#10587722)⋊C3
unambiguous semidirect product(C11×#10587723)⋊C3

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C32
derived, HallC7×C13 ⋊ C2×C32×C11
HallC11×ΓL(1,𝔽8)×C13⋊C3 ⋊ C2
HallC11×D91 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ C2×C11
HallD91 ⋊ C32×C11
HallC11×C13 ⋊ C3×AGL(1,𝔽7)
HallC7×C11 ⋊ C3×D13⋊C3
SylowC13 ⋊ C3×C11×AGL(1,𝔽7)
SylowC7 ⋊ C3×C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊(D13⋊C3)
commutator, cosocle, hypocenterC7×C13C2×C32×C11
FrattiniC1G
Fitting, socleC7×C11×C13C2×C32
LCSG ▷ C7×C13
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1001

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×D13⋊C3, D11×ΓL(1,𝔽8)⋊(D13⋊C3), (C11⋊AGL(1,𝔽7))⋊(D13⋊C3), …
maximal normal subgroup ofC11×AGL(1,𝔽7)×D13⋊C3, D11×ΓL(1,𝔽8)⋊(D13⋊C3), (C11⋊AGL(1,𝔽7))⋊(D13⋊C3), …
maximal quotient ofC11×ΓL(1,𝔽8)⋊(Dic13⋊C3), C2×C11×ΓL(1,𝔽8)⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 50);