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C3×C5×C17⋊AGL(1,𝔽7) #24924212

order10710
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C17⋊AGL(1,𝔽7)
unambiguous semidirect productC17⋊(C3×C5×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C5×D17)
unambiguous semidirect productD119⋊(C32×C5)
unambiguous semidirect product(C3×D119)⋊(C3×C5)
unambiguous semidirect product(C5×D119)⋊C32
unambiguous semidirect product(C3×C5×D119)⋊C3

Splittings

Fitting, socleC3×C5×C7×C17 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C32×C5
HallC3×C5×C17×ΓL(1,𝔽8) ⋊ C2
HallC5×D119 ⋊ C32
HallC3×C17×ΓL(1,𝔽8) ⋊ C2×C5
HallC5×C7×C17 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ D17
HallD119 ⋊ C32×C5
HallC5×C17 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C5×D17
HallC5×C7 ⋊ C32×D17
SylowC17 ⋊ C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C32×C5×D17

Subgroups

subgroupG/H
center, hypercenterC3×C5C17⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C17C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

705 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D17×AGL(1,𝔽7), C3×D5×C17⋊AGL(1,𝔽7), C3×D85⋊AGL(1,𝔽7), …
maximal normal subgroup ofC3×C5×D17×AGL(1,𝔽7), C3×D5×C17⋊AGL(1,𝔽7), C3×D85⋊AGL(1,𝔽7), …
maximal quotient ofC3×C5×ΓL(1,𝔽8)⋊Dic17, C2×C3×C5×C17⋊AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 27);