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C83×C5⋊AGL(1,𝔽7) #31775243

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

Aliases

direct productC83×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(AGL(1,𝔽7)×C83)
unambiguous semidirect productΓL(1,𝔽8)⋊(D5×C83)
unambiguous semidirect productD35⋊(C3×C83)
unambiguous semidirect product(D35×C83)⋊C3

Splittings

Fitting, socle, HallC5×C7×C83 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C83
HallC5×ΓL(1,𝔽8)×C83 ⋊ C2
HallD35×C83 ⋊ C3
HallΓL(1,𝔽8)×C83 ⋊ D5
HallC7×C83 ⋊ C3×D5
HallC5×C83 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×C83
HallD35 ⋊ C3×C83
HallΓL(1,𝔽8) ⋊ D5×C83
SylowC7 ⋊ C3×D5×C83
SylowC5 ⋊ AGL(1,𝔽7)×C83

Subgroups

subgroupG/H
center, hypercenterC83C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C3×C83
FrattiniC1G
Fitting, socleC5×C7×C83C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2905

Conjugacy classes & character table

1411 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD83×C5⋊AGL(1,𝔽7), D5×AGL(1,𝔽7)×C83, (C5⋊AGL(1,𝔽7))⋊D83, …
maximal normal subgroup ofD83×C5⋊AGL(1,𝔽7), D5×AGL(1,𝔽7)×C83, (C5⋊AGL(1,𝔽7))⋊D83, …
maximal quotient ofC83×ΓL(1,𝔽8)⋊Dic5, C2×C83×C5⋊AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 23);