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C3×C17×C5⋊AGL(1,𝔽7) #24924214

order10710
isoclinismisoclinic class of C5⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(C3×C17×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D5×C17)
unambiguous semidirect productD35⋊(C32×C17)
unambiguous semidirect product(C3×D35)⋊(C3×C17)
unambiguous semidirect product(C17×D35)⋊C32
unambiguous semidirect product(C3×C17×D35)⋊C3

Splittings

Fitting, socleC3×C5×C7×C17 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C32×C17
HallC3×C5×C17×ΓL(1,𝔽8) ⋊ C2
HallC17×D35 ⋊ C32
HallC3×C17×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×C17 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C17
HallC7×C17 ⋊ C32×D5
HallC5×C17 ⋊ C3×AGL(1,𝔽7)
HallD35 ⋊ C32×C17
HallC3×ΓL(1,𝔽8) ⋊ D5×C17
SylowC7 ⋊ C32×D5×C17
SylowC5 ⋊ C3×C17×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC3×C17C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C32×C17
FrattiniC1G
Fitting, socleC3×C5×C7×C17C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

867 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D17×C5⋊AGL(1,𝔽7), C3×D5×C17×AGL(1,𝔽7), C3×D85⋊AGL(1,𝔽7), …
maximal normal subgroup ofC3×D17×C5⋊AGL(1,𝔽7), C3×D5×C17×AGL(1,𝔽7), C3×D85⋊AGL(1,𝔽7), …
maximal quotient ofC3×C17×ΓL(1,𝔽8)⋊Dic5, C2×C3×C17×C5⋊AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 29);