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C2×AGL(1,𝔽7)×C73 #20259508

order6132
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C3×C73 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽7)×C73
unambiguous semidirect productD7⋊(C2×C3×C73)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C73)
unambiguous semidirect product(C2×D7)⋊(C3×C73)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C73)

Splittings

Fitting, socleC2×C7×C73 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C73
HallC2×D7×C73 ⋊ C3
HallΓL(1,𝔽8)×C73 ⋊ C22
HallC7×C73 ⋊ C22×C3
HallC2×D7 ⋊ C3×C73
HallΓL(1,𝔽8) ⋊ C22×C73

Subgroups

subgroupG/H
center, hypercenterC2×C73AGL(1,𝔽7)
commutator, hypocenterC7C22×C3×C73
FrattiniC1G
Fitting, socleC2×C7×C73C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C73

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1022 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×C73⋊C3, D3×AGL(1,𝔽7)×C73, C2×C3×AGL(1,𝔽7)×C73, …
maximal normal subgroup ofC2×AGL(1,𝔽7)×C73⋊C3, C2×C3×AGL(1,𝔽7)×C73, C2×C5×AGL(1,𝔽7)×C73
maximal quotient ofC2×C73×D7⋊C9, D3×AGL(1,𝔽7)×C73, C2×C3×AGL(1,𝔽7)×C73, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6132, 39);