Finite Group Databasebeta

← Prev (#22604661) Next (#22604663) →

C13×C17⋊AGL(1,𝔽7) #22604662

order9282
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C17⋊AGL(1,𝔽7)
unambiguous semidirect productC17⋊(C13×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C13×D17)
unambiguous semidirect productD119⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C3×C13
HallC13×C17×ΓL(1,𝔽8) ⋊ C2
HallC13×D119 ⋊ C3
HallC17×ΓL(1,𝔽8) ⋊ C2×C13
HallC13×ΓL(1,𝔽8) ⋊ D17
HallD119 ⋊ C3×C13
HallC13×C17 ⋊ AGL(1,𝔽7)
HallC7×C13 ⋊ C3×D17
HallΓL(1,𝔽8) ⋊ C13×D17
SylowC17 ⋊ C13×AGL(1,𝔽7)
SylowC7 ⋊ C3×C13×D17

Subgroups

subgroupG/H
center, hypercenterC13C17⋊AGL(1,𝔽7)
commutator, hypocenterC7×C17C2×C3×C13
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

611 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×D17×AGL(1,𝔽7), D13×C17⋊AGL(1,𝔽7), (ΓL(1,𝔽8)⋊D13)⋊D17, …
maximal normal subgroup ofC13×D17×AGL(1,𝔽7), D13×C17⋊AGL(1,𝔽7), (ΓL(1,𝔽8)⋊D13)⋊D17, …
maximal quotient ofC13×ΓL(1,𝔽8)⋊Dic17, C2×C13×C17⋊AGL(1,𝔽7), C13×C17⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 38);