Finite Group Databasebeta

← Prev (#34086177) Next (#34086179) →

C3×ΓL(1,𝔽8)⋊(D31⋊C5) #34086178

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊(D31⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×D31⋊C5)
unambiguous semidirect product(C3×ΓL(1,𝔽8)⋊D31)⋊C5

Splittings

Fitting, socleC3×C7×C31 ⋊ C2×C3×C5
derived, HallC7×C31 ⋊ C2×C32×C5
HallC3×ΓL(1,𝔽8)×ΓL(1,𝔽32) ⋊ C2
HallC3×ΓL(1,𝔽8)⋊D31 ⋊ C5
HallC7⋊(D31⋊C5) ⋊ C32
HallC3×ΓL(1,𝔽8)×C31 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C32
HallD217 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ D31⋊C5
SylowC31 ⋊ C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C32×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)⋊(D31⋊C5)
commutator, cosocle, hypocenterC7×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 651

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 83);