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C2×C11⋊(ΓL(1,𝔽8)⋊D13) #26046518

order12012
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊(ΓL(1,𝔽8)⋊D13)
unambiguous semidirect product(C2×C11)⋊(ΓL(1,𝔽8)⋊D13)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊D143

Splittings

Fitting, socleC2×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C22×C3
HallC2×D1001 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C22
HallC13×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D13
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ C2×D143
SylowC13 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×ΓL(1,𝔽8)⋊D13
SylowC7 ⋊ C2×C3×D143

Subgroups

subgroupG/H
center, hypercenterC2C11⋊(ΓL(1,𝔽8)⋊D13)
commutator, cosocle, hypocenterC7×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

724 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊(ΓL(1,𝔽8)⋊(D13⋊C3)), D3×C11⋊(ΓL(1,𝔽8)⋊D13), C2×C3×C11⋊(ΓL(1,𝔽8)⋊D13), …
maximal normal subgroup ofC2×C11⋊(ΓL(1,𝔽8)⋊(D13⋊C3)), C2×C3×C11⋊(ΓL(1,𝔽8)⋊D13)
maximal quotient ofC2×C11⋊((C7⋊C9)⋊D13), D3×C11⋊(ΓL(1,𝔽8)⋊D13), C2×C3×C11⋊(ΓL(1,𝔽8)⋊D13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 108);