Finite Group Databasebeta

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C22⋊C4×C3⋊AGL(1,ℤ/9) #72220056

order2592
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productC22⋊C4×C3⋊AGL(1,ℤ/9)

Splittings

FittingC3×C22⋊C4×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC22C22×C3⋊AGL(1,ℤ/9)
commutatorC2×C3×C9C22×C3×C4
FrattiniC22×C3C22×C3×C3⋊D3
FittingC3×C22⋊C4×3−1+2C2
socleC22×C32C22×C3×D3
prime radicalC23×C3⋊AGL(1,ℤ/9)C2
cosocleC22×C3×C9C23×C3
hypercenterC22⋊C4C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×C22⋊C4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

1473 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22⋊C4×#92314, #120×C3⋊AGL(1,ℤ/9), #72220150, …
maximal normal subgroup of#120×C3⋊AGL(1,ℤ/9), #72220150, C4×D4×C3⋊AGL(1,ℤ/9)
maximal quotient ofC22⋊C4×#92314, #102×C3⋊AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.