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(ΓL(1,𝔽8)⋊D13)⋊D17 #32915495

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

Aliases

unambiguous semidirect product(ΓL(1,𝔽8)⋊D13)⋊D17
unambiguous semidirect product(C17⋊AGL(1,𝔽7))⋊D13

Splittings

Fitting, socle, derived, HallC7×C13×C17 ⋊ C22×C3
HallD91⋊D17 ⋊ C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C22
HallC17×ΓL(1,𝔽8) ⋊ C2×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×D17
HallC13×C17 ⋊ C2×AGL(1,𝔽7)
HallC7×C17 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×D17
HallΓL(1,𝔽8) ⋊ D13×D17
SylowC17 ⋊ D13×AGL(1,𝔽7)
SylowC13 ⋊ D17×AGL(1,𝔽7)
SylowC7 ⋊ C3×D13×D17

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C17C22×C3
LCSG ▷ C7×C13×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1547

Polycyclic presentation:

2^2,3,7,13,17|e^a=e^12,f^a=f^16,d^b=d^6,e^b=e^12,d^c=d^2

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 90);