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C2×C5×ΓL(1,𝔽8)×C167 #46856375

order35070
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C167 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C167
unambiguous semidirect product(C2×C7)⋊(C3×C5×C167)
unambiguous semidirect product(C2×C5×C7)⋊(C3×C167)
unambiguous semidirect product(C2×C7×C167)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×C167)⋊C3

Splittings

Fitting, socle, HallC2×C5×C7×C167 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C5×C167
HallC5×C7×C167 ⋊ C2×C3
HallC2×C7×C167 ⋊ C3×C5
HallC7×C167 ⋊ C2×C3×C5
HallC2×C5×C7 ⋊ C3×C167
HallC5×C7 ⋊ C2×C3×C167
HallC2×C7 ⋊ C3×C5×C167

Subgroups

subgroupG/H
center, hypercenterC2×C5×C167ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C5×C167
FrattiniC1G
Fitting, socleC2×C5×C7×C167C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C167

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11690

Conjugacy classes & character table

8350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35070, 2);