Finite Group Databasebeta

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#103×AGL(1,ℤ/9) #13141946

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct product#103×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C3×#103)
unambiguous semidirect product(D9×#103)⋊C3

Splittings

Fitting3−1+2×#103 ⋊ C2
Sylow3−1+2 ⋊ C2×#103

Subgroups

subgroupG/H
centerC22D4×AGL(1,ℤ/9)
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
Fitting3−1+2×#103C2
socleC22×C3C3×D3×D4
prime radicalC22×AGL(1,ℤ/9)D4
cosocleC2×C4×C9C23×C3
hypercenter#103AGL(1,ℤ/9)
hypocenterC9C2×C3×#103
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

507 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8009);