Finite Group Databasebeta

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3−1+2×AGL(1,𝔽19) #72244841

order9234
automorphism?
homologyAbelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×AGL(1,𝔽19)

Splittings

FittingC19×3−1+2 ⋊ C2×C9
Hall3−1+2×#4296 ⋊ C2
HallD19 ⋊ C9×3−1+2
SylowC19 ⋊ C2×C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×AGL(1,𝔽19)
commutator, socleC3×C19C2×C32×C9
FittingC19×3−1+2C2×C9
prime radicalC32×D19⋊C3C32
cosocleC3×C19⋊C3C2×C33
hypercenter3−1+2AGL(1,𝔽19)
hypocenterC19C2×C9×3−1+2
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ 3−1+2

296 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 171

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×AGL(1,𝔽19)
maximal normal subgroup ofAGL(1,ℤ/9)×AGL(1,𝔽19)

GAP

Past the SmallGroups library coverage — no SmallGroups id.