Finite Group Databasebeta

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C2×#100×AGL(1,ℤ/9) #72244665

order3456
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#100×AGL(1,ℤ/9)

Splittings

FittingC2×3−1+2×#100 ⋊ C2
Sylow3−1+2 ⋊ C22×#100

Subgroups

subgroupG/H
centerC22C22⋊C4×AGL(1,ℤ/9)
commutatorC22×C9C23×C3×C4
FrattiniC2×C3×C4C23×C3×D3
FittingC2×3−1+2×#100C2
socleC22×C3C3×D3×C22⋊C4
prime radicalC22×D4×AGL(1,ℤ/9)C2
cosocleC2×C4×C9C24×C3
hypercenterC2×#100AGL(1,ℤ/9)
hypocenterC9C22×C3×#100
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

3069 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,ℤ/9)×#453
maximal normal subgroup ofC2×AGL(1,ℤ/9)×#453

GAP

Past the SmallGroups library coverage — no SmallGroups id.