Finite Group Databasebeta

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C22×D5×AGL(1,ℤ/9) #72247331

order2160
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC22×D5×AGL(1,ℤ/9)

Splittings

FittingC22×C5×3−1+2 ⋊ C22
derivedC5×C9 ⋊ C24×C3
HallC5×3−1+2 ⋊ C24
Sylow3−1+2 ⋊ C23×D5
SylowC5 ⋊ C23×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC22D5×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC5×C9C24×C3
FrattiniC3C22×C3×D3×D5
FittingC22×C5×3−1+2C22
socleC22×C3×C5C2×C3×D3
LCSG ▷ C5×C9
UCSC1 ◁ C22

836 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 229 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 ofC22×AGL(1,𝔽5)×AGL(1,ℤ/9), C22×C5⋊D5×AGL(1,ℤ/9), D4×D5×AGL(1,ℤ/9), …
maximal normal subgroup ofC22×AGL(1,𝔽5)×AGL(1,ℤ/9), D4×D5×AGL(1,ℤ/9), AGL(1,ℤ/9)×C22⋊AGL(1,𝔽5), …
maximal quotient ofC22×C5⋊D5×AGL(1,ℤ/9), D4×D5×AGL(1,ℤ/9), C2×D52×AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.