Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2×C17 |
| unambiguous semidirect product | C22⋊#14579585 |
| Fitting, socle, derived, Hall | C22×C172 ⋊ C9 |
| Sylow | C172 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ #14579585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C172 | C9 |
| prime radical, cosocle | C22×C172⋊C3 | C3 |
| LCS | G ▷ C22×C172 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,2^2,17^2|a^3=b,c^a=d,d^a=cd,e^a=e^2f^10,f^a=e^4f^12,e^b=e^2f^12,f^b=e^15f^14140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 107);