Finite Group Databasebeta

← Prev (#24924210) Next (#24924212) →

C3×C5×C17×AGL(1,𝔽7) #24924211

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

Aliases

direct productC3×C5×C17×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C32×C5×C17)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C3×C5×C17)
unambiguous semidirect product(C3×D7)⋊(C3×C5×C17)
unambiguous semidirect product(C5×D7)⋊(C32×C17)
unambiguous semidirect product(C3×C5×D7)⋊(C3×C17)
unambiguous semidirect product(D7×C17)⋊(C32×C5)
unambiguous semidirect product(C3×D7×C17)⋊(C3×C5)
unambiguous semidirect product(C5×D7×C17)⋊C32
unambiguous semidirect product(C3×C5×D7×C17)⋊C3

Splittings

Fitting, socleC3×C5×C7×C17 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C32×C5×C17
HallC3×C5×C17×ΓL(1,𝔽8) ⋊ C2
HallC5×D7×C17 ⋊ C32
HallC3×C17×ΓL(1,𝔽8) ⋊ C2×C5
HallC5×C7×C17 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C17
HallD7×C17 ⋊ C32×C5
HallC7×C17 ⋊ C2×C32×C5
HallC5×D7 ⋊ C32×C17
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C17
HallC5×C7 ⋊ C2×C32×C17
HallD7 ⋊ C32×C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C32×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C7×C17C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D17×AGL(1,𝔽7), C3×D5×C17×AGL(1,𝔽7), C3×AGL(1,𝔽7)×D85, …
maximal normal subgroup ofC3×C5×D17×AGL(1,𝔽7), C3×D5×C17×AGL(1,𝔽7), C3×AGL(1,𝔽7)×D85, …
maximal quotient ofC3×C5×C17×ΓL(1,𝔽8)⋊C4, C2×C3×C5×C17×AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 26);