Finite Group Databasebeta

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D3×D9×AGL(1,𝔽5) #72222415

order2160
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD3×D9×AGL(1,𝔽5)

Splittings

Fitting, derived, HallC3×C5×C9 ⋊ C22×C4
SylowC3×C9 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C4×D3×D9

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC3×C5×C9C22×C4
FrattiniC3D32×AGL(1,𝔽5)
socleC32×C5C2×C4×D3
prime radicalD3×D5×D9C2
cosocleC3×C9×D5C23
LCSG ▷ C3×C5×C9
UCSC1

356 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 70 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

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD92×AGL(1,𝔽5), D3×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×((C3⋊D3)⋊C9)⋊C2, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/9)
maximal quotient ofD92×AGL(1,𝔽5), AGL(1,𝔽5)×((C3⋊D3)⋊C9)⋊C2, D9×AGL(1,𝔽5)×S4

GAP

Past the SmallGroups library coverage — no SmallGroups id.