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C3×ΓL(1,𝔽8)⋊D89 #26014248

order11214
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊D89
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D89)
unambiguous semidirect productC89⋊(C3×AGL(1,𝔽7))
unambiguous semidirect productD623⋊C32
unambiguous semidirect product(C3×D623)⋊C3

Splittings

Fitting, socleC3×C7×C89 ⋊ C2×C3
derived, HallC7×C89 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)×C89 ⋊ C2
HallD623 ⋊ C32
SylowC89 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ D89
SylowC7 ⋊ C32×D89

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)⋊D89
commutator, cosocle, hypocenterC7×C89C2×C32
FrattiniC1G
Fitting, socleC3×C7×C89C2×C3
LCSG ▷ C7×C89
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

681 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D89, D3×ΓL(1,𝔽8)⋊D89, (C3⋊AGL(1,𝔽7))⋊D89, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D89, D3×ΓL(1,𝔽8)⋊D89, (C3⋊AGL(1,𝔽7))⋊D89, …
maximal quotient ofC3×ΓL(1,𝔽8)⋊Dic89, C2×C3×ΓL(1,𝔽8)⋊D89

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11214, 15);