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C5×AGL(1,𝔽7)×C83 #31775239

order17430
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C83 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽7)×C83
unambiguous semidirect productD7⋊(C3×C5×C83)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C83)
unambiguous semidirect product(C5×D7)⋊(C3×C83)
unambiguous semidirect product(D7×C83)⋊(C3×C5)
unambiguous semidirect product(C5×D7×C83)⋊C3

Splittings

Fitting, socle, HallC5×C7×C83 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C83
HallC5×ΓL(1,𝔽8)×C83 ⋊ C2
HallC5×D7×C83 ⋊ C3
HallΓL(1,𝔽8)×C83 ⋊ C2×C5
HallD7×C83 ⋊ C3×C5
HallC7×C83 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C83
HallC5×D7 ⋊ C3×C83
HallC5×C7 ⋊ C2×C3×C83
HallΓL(1,𝔽8) ⋊ C2×C5×C83
HallD7 ⋊ C3×C5×C83

Subgroups

subgroupG/H
center, hypercenterC5×C83AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C83
FrattiniC1G
Fitting, socleC5×C7×C83C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2905

Conjugacy classes & character table

2905 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D83, D5×AGL(1,𝔽7)×C83, AGL(1,𝔽7)×D415, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D83, D5×AGL(1,𝔽7)×C83, AGL(1,𝔽7)×D415, …
maximal quotient ofC5×C83×ΓL(1,𝔽8)⋊C4, C2×C5×AGL(1,𝔽7)×C83

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 19);