Finite Group Databasebeta

← Prev (#46828632) Next (#46828634) →

C2×C3×ΓL(1,𝔽8)×D137 #46828633

order34524
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×ΓL(1,𝔽8)×D137
unambiguous semidirect productC137⋊(C22×C3×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C137)⋊(C2×C3×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D137)⋊C32
unambiguous semidirect product(C2×C3×C7×D137)⋊C3

Splittings

Fitting, socleC2×C3×C7×C137 ⋊ C2×C3
derived, HallC7×C137 ⋊ C22×C32
HallC3×ΓL(1,𝔽8)×C137 ⋊ C22
HallC2×C7×D137 ⋊ C32
SylowC137 ⋊ C22×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C32×D137

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D137
commutator, cosocle, hypocenterC7×C137C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C137C2×C3
LCSG ▷ C7×C137
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5754

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 76);