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C2×C3×ΓL(1,𝔽8)×C71 #22582141

order8946
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C32×C71 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×ΓL(1,𝔽8)×C71
unambiguous semidirect product(C2×C7)⋊(C32×C71)
unambiguous semidirect product(C2×C3×C7)⋊(C3×C71)
unambiguous semidirect product(C2×C7×C71)⋊C32
unambiguous semidirect product(C2×C3×C7×C71)⋊C3

Splittings

Fitting, socleC2×C3×C7×C71 ⋊ C3
derived, SylowC7 ⋊ C2×C32×C71
HallC2×C7×C71 ⋊ C32
HallC7×C71 ⋊ C2×C32
HallC2×C7 ⋊ C32×C71

Subgroups

subgroupG/H
center, hypercenterC2×C3×C71ΓL(1,𝔽8)
commutator, hypocenterC7C2×C32×C71
FrattiniC1G
Fitting, socleC2×C3×C7×C71C3
LCSG ▷ C7
UCSC1 ◁ C2×C3×C71

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2130 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C71×ΓL(1,𝔽8)⋊C4, C3×ΓL(1,𝔽8)⋊Dic71, C3×ΓL(1,𝔽8)×Dic71, …
maximal normal subgroup ofC3×C71×ΓL(1,𝔽8)⋊C4, C3×ΓL(1,𝔽8)⋊Dic71, C3×ΓL(1,𝔽8)×Dic71, …
maximal quotient ofC3×C4×ΓL(1,𝔽8)×C71, C22×C3×ΓL(1,𝔽8)×C71

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8946, 31);