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C17×C11⋊AGL(1,𝔽7) #21463285

order7854
isoclinismisoclinic class of C11⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C11⋊AGL(1,𝔽7)
unambiguous semidirect productC11⋊(C17×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×D11)
unambiguous semidirect productD77⋊(C3×C17)
unambiguous semidirect product(C17×D77)⋊C3

Splittings

Fitting, socle, HallC7×C11×C17 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C17
HallC11×C17×ΓL(1,𝔽8) ⋊ C2
HallC17×D77 ⋊ C3
HallC17×ΓL(1,𝔽8) ⋊ D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C17
HallC11×C17 ⋊ AGL(1,𝔽7)
HallD77 ⋊ C3×C17
HallC7×C17 ⋊ C3×D11
HallΓL(1,𝔽8) ⋊ C17×D11
SylowC11 ⋊ C17×AGL(1,𝔽7)
SylowC7 ⋊ C3×C17×D11

Subgroups

subgroupG/H
center, hypercenterC17C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C2×C3×C17
FrattiniC1G
Fitting, socleC7×C11×C17C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×D11×AGL(1,𝔽7), D187⋊AGL(1,𝔽7), D17×C11⋊AGL(1,𝔽7), …
maximal normal subgroup ofC17×D11×AGL(1,𝔽7), D187⋊AGL(1,𝔽7), D17×C11⋊AGL(1,𝔽7), …
maximal quotient ofC17×C11⋊(ΓL(1,𝔽8)⋊C4), C2×C17×C11⋊AGL(1,𝔽7), C17×C11⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7854, 23);