Finite Group Databasebeta

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C2×AGL(1,ℤ/8)×C3⋊D9 #72244708

order3456
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29×C3

Aliases

direct productC2×AGL(1,ℤ/8)×C3⋊D9

Splittings

FittingC2×C3×C9×AGL(1,ℤ/8) ⋊ C2
SylowC3×C9 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×C3⋊D9
commutator, cosocleC3×C4×C9C25
FrattiniC3×C4C24×C3⋊D3
FittingC2×C3×C9×AGL(1,ℤ/8)C2
socleC22×C32C2×D3×D4
hypercenterC2×AGL(1,ℤ/8)C3⋊D9
hypocenterC3×C9C22×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

8600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/8)×C9⋊D9
maximal quotient ofC2×AGL(1,ℤ/8)×C9⋊D9

GAP

Past the SmallGroups library coverage — no SmallGroups id.