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C3×AGL(1,𝔽7)×C43 #19129368

order5418
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C32×C43 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,𝔽7)×C43
unambiguous semidirect productD7⋊(C32×C43)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C3×C43)
unambiguous semidirect product(C3×D7)⋊(C3×C43)

Splittings

Fitting, socleC3×C7×C43 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C32×C43
HallC3×ΓL(1,𝔽8)×C43 ⋊ C2
HallD7×C43 ⋊ C32
HallC7×C43 ⋊ C2×C32
HallC3×ΓL(1,𝔽8) ⋊ C2×C43
HallD7 ⋊ C32×C43

Subgroups

subgroupG/H
center, hypercenterC3×C43AGL(1,𝔽7)
commutator, hypocenterC7C2×C32×C43
FrattiniC1G
Fitting, socleC3×C7×C43C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

903 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D43, D3×AGL(1,𝔽7)×C43, AGL(1,𝔽7)×D129, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D43, D3×AGL(1,𝔽7)×C43, AGL(1,𝔽7)×D129, …
maximal quotient ofC3×C43×ΓL(1,𝔽8)⋊C4, C2×C3×AGL(1,𝔽7)×C43, C3×C5×AGL(1,𝔽7)×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5418, 47);