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C13×C17×AGL(1,𝔽7) #22604658

order9282
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC13×C17×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C13×C17)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C13×C17)
unambiguous semidirect product(D7×C17)⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C13×C17
HallC13×C17×ΓL(1,𝔽8) ⋊ C2
HallC13×D7×C17 ⋊ C3
HallC17×ΓL(1,𝔽8) ⋊ C2×C13
HallC13×ΓL(1,𝔽8) ⋊ C2×C17
HallD7×C17 ⋊ C3×C13
HallC13×D7 ⋊ C3×C17
HallC7×C17 ⋊ C2×C3×C13
HallC7×C13 ⋊ C2×C3×C17
HallΓL(1,𝔽8) ⋊ C2×C13×C17
HallD7 ⋊ C3×C13×C17

Subgroups

subgroupG/H
center, hypercenterC13×C17AGL(1,𝔽7)
commutator, hypocenterC7C2×C3×C13×C17
FrattiniC1G
Fitting, socleC7×C13×C17C2×C3
LCSG ▷ C7
UCSC1 ◁ C13×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1547 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×D17×AGL(1,𝔽7), C17×D13×AGL(1,𝔽7), AGL(1,𝔽7)×D221, …
maximal normal subgroup ofC13×D17×AGL(1,𝔽7), C17×D13×AGL(1,𝔽7), AGL(1,𝔽7)×D221, …
maximal quotient ofC13×C17×ΓL(1,𝔽8)⋊C4, C2×C13×C17×AGL(1,𝔽7), C13×C17×D7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 34);