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C3×ΓL(1,𝔽8)×D71 #22582136

order8946
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D71
unambiguous semidirect productC71⋊(C2×C3×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D71)⋊C32
unambiguous semidirect product(C3×C7×D71)⋊C3

Splittings

Fitting, socleC3×C7×C71 ⋊ C2×C3
derived, HallC7×C71 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)×C71 ⋊ C2
HallC7×D71 ⋊ C32
SylowC71 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D71

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D71
commutator, hypocenterC7×C71C2×C32
FrattiniC1G
Fitting, socleC3×C7×C71C2×C3
LCSG ▷ C7×C71
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

555 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D71, C3⋊AGL(1,𝔽7)×D71, D3×ΓL(1,𝔽8)×D71, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D71, C3⋊AGL(1,𝔽7)×D71, D3×ΓL(1,𝔽8)×D71, …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic71, C2×C3×ΓL(1,𝔽8)×D71

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8946, 26);