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C17×ΓL(1,𝔽8)⋊D47 #46776771

order33558
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)⋊D47
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×D47)
unambiguous semidirect productC47⋊(C17×AGL(1,𝔽7))
unambiguous semidirect productD329⋊(C3×C17)
unambiguous semidirect product(C17×D329)⋊C3

Splittings

Fitting, socle, HallC7×C17×C47 ⋊ C2×C3
derived, HallC7×C47 ⋊ C2×C3×C17
HallC17×ΓL(1,𝔽8)×C47 ⋊ C2
HallC17×D329 ⋊ C3
HallΓL(1,𝔽8)×C47 ⋊ C2×C17
HallC17×C47 ⋊ AGL(1,𝔽7)
HallD329 ⋊ C3×C17
HallC17×ΓL(1,𝔽8) ⋊ D47
HallC7×C17 ⋊ C3×D47
SylowC47 ⋊ C17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C17×D47
SylowC7 ⋊ C3×C17×D47

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)⋊D47
commutator, cosocle, hypocenterC7×C47C2×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C47C2×C3
LCSG ▷ C7×C47
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5593

Conjugacy classes & character table

2074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33558, 22);