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D17×C11⋊AGL(1,𝔽7) #30628112

order15708
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD17×C11⋊AGL(1,𝔽7)
unambiguous semidirect product(C11×D17)⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)×D17)⋊D11
unambiguous semidirect product(D17×D77)⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C17 ⋊ C22×C3
HallD17×D77 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C22
HallC17×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D17
HallC11×C17 ⋊ C2×AGL(1,𝔽7)
HallC7×C17 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D17
HallΓL(1,𝔽8) ⋊ D11×D17
SylowC17 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ D17×AGL(1,𝔽7)
SylowC7 ⋊ C3×D11×D17

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C17C22×C3
LCSG ▷ C7×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1309

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 33);