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A4×ΓL(1,𝔽8)×C137 #46828630

order34524
automorphism?
homologyAbelianization (H1) = C32×C137 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×ΓL(1,𝔽8)×C137
unambiguous semidirect product(C22×ΓL(1,𝔽8))⋊(C3×C137)
unambiguous semidirect product(C7×A4)⋊(C3×C137)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8))⋊(C3×C137)
unambiguous semidirect product(C22⋊ΓL(1,𝔽8)×C137)⋊C3
unambiguous semidirect product(C7×A4×C137)⋊C3
unambiguous semidirect product(C22×ΓL(1,𝔽8)×C137)⋊C3

Splittings

Fitting, socle, HallC22×C7×C137 ⋊ C32
derived, HallC22×C7 ⋊ C32×C137
HallC7×C137 ⋊ C3×A4
HallC22×C137 ⋊ C3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×A4×C137
SylowC22 ⋊ C3×ΓL(1,𝔽8)×C137

Subgroups

subgroupG/H
center, hypercenterC137A4×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C137
FrattiniC1G
Fitting, socleC22×C7×C137C32
LCSG ▷ C22×C7
UCSC1 ◁ C137

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3836

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 73);