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C167×C5⋊AGL(1,𝔽7) #46856396

order35070
automorphism?
homologyAbelianization (H1) = C2×C3×C167 · Schur multiplier (H2) = C1

Aliases

direct productC167×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(AGL(1,𝔽7)×C167)
unambiguous semidirect productΓL(1,𝔽8)⋊(D5×C167)
unambiguous semidirect productD35⋊(C3×C167)
unambiguous semidirect product(D35×C167)⋊C3

Splittings

Fitting, socle, HallC5×C7×C167 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C167
HallC5×ΓL(1,𝔽8)×C167 ⋊ C2
HallD35×C167 ⋊ C3
HallΓL(1,𝔽8)×C167 ⋊ D5
HallC7×C167 ⋊ C3×D5
HallC5×C167 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×C167
HallD35 ⋊ C3×C167
HallΓL(1,𝔽8) ⋊ D5×C167
SylowC7 ⋊ C3×D5×C167
SylowC5 ⋊ AGL(1,𝔽7)×C167

Subgroups

subgroupG/H
center, hypercenterC167C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C3×C167
FrattiniC1G
Fitting, socleC5×C7×C167C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C167

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5845

Conjugacy classes & character table

2839 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35070, 23);