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C13×ΓL(1,𝔽8)×D11 #20238798

order6006
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×D11
unambiguous semidirect productC11⋊(C2×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D11)⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C13
HallC11×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×C13×D11 ⋊ C3
HallC11×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×D11 ⋊ C3×C13
HallC11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×D11
SylowC11 ⋊ C2×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×D11

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C2×C3×C13
FrattiniC1G
Fitting, socleC7×C11×C13C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D11×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D13, ΓL(1,𝔽8)×D11×D13, …
maximal normal subgroup ofC13×D11×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D13, ΓL(1,𝔽8)×D11×D13, …
maximal quotient ofC13×ΓL(1,𝔽8)×Dic11, C2×C13×ΓL(1,𝔽8)×D11, C13×D11×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6006, 26);