Finite Group Databasebeta

← Prev (#34086201) Next (#34086203) →

C5×AGL(1,𝔽7)×C31⋊C3 #34086202

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

Aliases

direct productC5×AGL(1,𝔽7)×C31⋊C3
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C31⋊C3)
unambiguous semidirect product(C5×D7×C31⋊C3)⋊C3
unambiguous semidirect product(C5×C31×AGL(1,𝔽7))⋊C3
unambiguous semidirect product(C5×#13049959)⋊C3
unambiguous semidirect product(C5×#13049958)⋊C3

Splittings

Fitting, socle, HallC5×C7×C31 ⋊ C2×C32
derived, HallC7×C31 ⋊ C2×C32×C5
HallC5×ΓL(1,𝔽8)×C31⋊C3 ⋊ C2
HallC5×D7×C31 ⋊ C32
HallΓL(1,𝔽8)×C31⋊C3 ⋊ C2×C5
HallD7×C31 ⋊ C32×C5
HallC5×C31 ⋊ C3×AGL(1,𝔽7)
HallC5×D7 ⋊ C3×C31⋊C3
HallC5×C7 ⋊ C2×C3×C31⋊C3
SylowC31 ⋊ C3×C5×AGL(1,𝔽7)
HallD7 ⋊ C3×C5×C31⋊C3
SylowC7 ⋊ C2×C3×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5AGL(1,𝔽7)×C31⋊C3
commutator, cosocle, hypocenterC7×C31C2×C32×C5
FrattiniC1G
Fitting, socleC5×C7×C31C2×C32
LCSG ▷ C7×C31
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1085

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 107);