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ΓL(1,𝔽8)×D11×D17 #30628115

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

Aliases

direct productΓL(1,𝔽8)×D11×D17
unambiguous semidirect product(C17×D11)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C11×D17)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect productD187⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D11×D17)⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C17 ⋊ C22×C3
HallC7×D11×D17 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C22
HallC17×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D17
HallC11×C17 ⋊ C22×ΓL(1,𝔽8)
HallC7×C17 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D17
SylowC17 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×ΓL(1,𝔽8)×D17
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 36);