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C47×C17⋊AGL(1,𝔽7) #46776772

order33558
automorphism?
homologyAbelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×C17⋊AGL(1,𝔽7)
unambiguous semidirect productC17⋊(AGL(1,𝔽7)×C47)
unambiguous semidirect productΓL(1,𝔽8)⋊(D17×C47)
unambiguous semidirect productD119⋊(C3×C47)
unambiguous semidirect product(C47×D119)⋊C3

Splittings

Fitting, socle, HallC7×C17×C47 ⋊ C2×C3
derived, HallC7×C17 ⋊ C2×C3×C47
HallC17×ΓL(1,𝔽8)×C47 ⋊ C2
HallC47×D119 ⋊ C3
HallΓL(1,𝔽8)×C47 ⋊ D17
HallC17×C47 ⋊ AGL(1,𝔽7)
HallC17×ΓL(1,𝔽8) ⋊ C2×C47
HallC7×C47 ⋊ C3×D17
HallD119 ⋊ C3×C47
HallΓL(1,𝔽8) ⋊ D17×C47
SylowC17 ⋊ AGL(1,𝔽7)×C47
SylowC7 ⋊ C3×D17×C47

Subgroups

subgroupG/H
center, hypercenterC47C17⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C2×C3×C47
FrattiniC1G
Fitting, socleC7×C17×C47C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5593

Conjugacy classes & character table

2209 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33558, 23);