Finite Group Databasebeta

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C2×C4⋊C4×AGL(1,ℤ/9) #13152453

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C4⋊C4×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C2×C3×C4⋊C4)
unambiguous semidirect product(C2×C4⋊C4×D9)⋊C3

Splittings

FittingC2×C4⋊C4×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC23C22×AGL(1,ℤ/9)
commutatorC2×C9C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC2×C4⋊C4×3−1+2C2
socleC23×C3C22×C3×D3
prime radicalC23×AGL(1,ℤ/9)C22
cosocleC22×C9C24×C3
hypercenterC2×C4⋊C4AGL(1,ℤ/9)
hypocenterC9C22×C3×C4⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4⋊C4

1300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18516);