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ΓL(1,𝔽8)×D17×D23 #45659271

order32844
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productΓL(1,𝔽8)×D17×D23
unambiguous semidirect product(C23×D17)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C17×D23)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect productD391⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D17×D23)⋊C3

Splittings

Fitting, socle, derived, HallC7×C17×C23 ⋊ C22×C3
HallC7×D17×D23 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C22
HallΓL(1,𝔽8)×C23 ⋊ C2×D17
HallC17×C23 ⋊ C22×ΓL(1,𝔽8)
HallC17×ΓL(1,𝔽8) ⋊ C2×D23
HallC7×C23 ⋊ C2×C3×D17
HallC7×C17 ⋊ C2×C3×D23
SylowC23 ⋊ C2×ΓL(1,𝔽8)×D17
SylowC17 ⋊ C2×ΓL(1,𝔽8)×D23
SylowC7 ⋊ C3×D17×D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C17×C23C22×C3
LCSG ▷ C7×C17×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 36);