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C19×AGL(1,𝔽31) #31799004

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C5×C19)
unambiguous semidirect product(D31⋊C5)⋊(C3×C19)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C2×C19)
unambiguous semidirect product(C19×D31⋊C3)⋊C5

Splittings

Fitting, socle, HallC19×C31 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C2×C3×C5×C19
HallC19×(C31⋊C3)⋊C5 ⋊ C2
HallC19×D31⋊C5 ⋊ C3
HallC19×D31⋊C3 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
HallC19×C31⋊C3 ⋊ C2×C5
HallC19×D31 ⋊ C3×C5
Hall(C31⋊C3)⋊C5 ⋊ C2×C19
HallD31⋊C5 ⋊ C3×C19
HallD31⋊C3 ⋊ C5×C19
HallΓL(1,𝔽32) ⋊ C2×C3×C19
HallC31⋊C3 ⋊ C2×C5×C19
HallD31 ⋊ C3×C5×C19

Subgroups

subgroupG/H
center, hypercenterC19AGL(1,𝔽31)
commutator, cosocle, hypocenterC31C2×C3×C5×C19
FrattiniC1G
Fitting, socleC19×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 589

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD19×AGL(1,𝔽31), C2×C19×AGL(1,𝔽31)
maximal normal subgroup ofD19×AGL(1,𝔽31), C2×C19×AGL(1,𝔽31)
maximal quotient ofC19×((C31⋊C3)⋊C4)⋊C5, C2×C19×AGL(1,𝔽31)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 61);