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ΓL(1,𝔽8)×D799 #46776769

order33558
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D799
unambiguous semidirect productC17⋊(ΓL(1,𝔽8)×D47)
unambiguous semidirect productC47⋊(ΓL(1,𝔽8)×D17)
unambiguous semidirect product(C7×D799)⋊C3

Splittings

Fitting, socle, derived, HallC7×C17×C47 ⋊ C2×C3
HallC17×ΓL(1,𝔽8)×C47 ⋊ C2
HallC7×D799 ⋊ C3
HallΓL(1,𝔽8)×C47 ⋊ D17
HallC17×C47 ⋊ C2×ΓL(1,𝔽8)
HallC17×ΓL(1,𝔽8) ⋊ D47
HallC7×C47 ⋊ C3×D17
HallC7×C17 ⋊ C3×D47
SylowC47 ⋊ ΓL(1,𝔽8)×D17
SylowC17 ⋊ ΓL(1,𝔽8)×D47
SylowC7 ⋊ C3×D799

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C17×C47C2×C3
LCSG ▷ C7×C17×C47
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5593

Conjugacy classes & character table

2005 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33558, 20);