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C22⋊C8×AGL(1,ℤ/9) #13141631

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C8×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C3×C22⋊C8)
unambiguous semidirect product(D9×C22⋊C8)⋊C3

Splittings

Fitting3−1+2×C22⋊C8 ⋊ C2
Sylow3−1+2 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC2×C4C22×AGL(1,ℤ/9)
commutatorC2×C9C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
Fitting3−1+2×C22⋊C8C2
socleC22×C3C2×C3×C4×D3
prime radicalC23×AGL(1,ℤ/9)C4
cosocleC2×C4×C9C23×C3
hypercenterC22⋊C8AGL(1,ℤ/9)
hypocenterC9C2×C3×C22⋊C8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22⋊C8

631 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

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, 7694);