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C2×C17×ΓL(1,𝔽8)⋊D13 #32915544

order18564
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×ΓL(1,𝔽8)⋊D13
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C17×D13)

Splittings

Fitting, socleC2×C7×C13×C17 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C17
HallC2×C17×D91 ⋊ C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C22
HallC7×C13×C17 ⋊ C22×C3
HallC2×D91 ⋊ C3×C17
HallC17×ΓL(1,𝔽8) ⋊ C2×D13
HallC13×ΓL(1,𝔽8) ⋊ C22×C17
HallC13×C17 ⋊ C2×AGL(1,𝔽7)
HallC7×C17 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ C2×C17×D13
SylowC13 ⋊ C2×C17×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C17×D13

Subgroups

subgroupG/H
center, hypercenterC2×C17ΓL(1,𝔽8)⋊D13
commutator, cosocle, hypocenterC7×C13C22×C3×C17
FrattiniC1G
Fitting, socleC2×C7×C13×C17C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3094

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 139);