Finite Group Databasebeta

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C4×D5×AGL(1,ℤ/9) #72247364

order2160
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D5×AGL(1,ℤ/9)

Splittings

FittingC4×C5×3−1+2 ⋊ C22
derivedC5×C9 ⋊ C22×C3×C4
HallC5×3−1+2 ⋊ C22×C4
Sylow3−1+2 ⋊ C2×C4×D5
SylowC5 ⋊ C2×C4×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC4D5×AGL(1,ℤ/9)
commutator, hypocenterC5×C9C22×C3×C4
FrattiniC2×C3C2×C3×D3×D5
FittingC4×C5×3−1+2C22
socleC2×C3×C5C22×C3×D3
prime radicalC2×D5×AGL(1,ℤ/9)C2
cosocleC2×C5×C9C23×C3
LCSG ▷ C5×C9
UCSC1 ◁ C4

340 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 103 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) = 180

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,𝔽5)×AGL(1,ℤ/9), D4×D5×AGL(1,ℤ/9), AGL(1,ℤ/9)×C4⋊AGL(1,𝔽5), …
maximal normal subgroup ofC4×AGL(1,𝔽5)×AGL(1,ℤ/9), D4×D5×AGL(1,ℤ/9), AGL(1,ℤ/9)×C4⋊AGL(1,𝔽5)
maximal quotient ofD5×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,ℤ/9)×#6036

GAP

Past the SmallGroups library coverage — no SmallGroups id.