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AGL(1,𝔽5)×C3⋊AGL(1,ℤ/9) #72222366

order3240
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productAGL(1,𝔽5)×C3⋊AGL(1,ℤ/9)

Splittings

Fitting, HallC3×C5×3−1+2 ⋊ C2×C4
derivedC3×C5×C9 ⋊ C2×C3×C4
SylowC3×3−1+2 ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C4×C3⋊AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC3×C5×C9C2×C3×C4
FrattiniC3C3×C3⋊D3×AGL(1,𝔽5)
FittingC3×C5×3−1+2C2×C4
socleC32×C5C3×C4×D3
prime radicalD5×C3⋊AGL(1,ℤ/9)C2
cosocleC3×C9×D5C22×C3
LCSG ▷ C3×C5×C9
UCSC1

374 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#92314, D3×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×#4207⋊C3, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×#4207⋊C3, AGL(1,𝔽5)×#4169⋊C3, …
maximal quotient ofAGL(1,𝔽5)×#92314, AGL(1,𝔽5)×#92302, AGL(1,𝔽5)×A4⋊AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.