Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#11923883 |
| Fitting, derived, Hall | C9×C172 ⋊ C4 |
| Sylow | C172 ⋊ Dic9 |
| Sylow | C9 ⋊ #11923883 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C172 | C4 |
| Frattini | C3 | C3⋊#11923883 |
| socle | C3×C172 | Dic3 |
| prime radical | C3×C17⋊D17 | D3 |
| cosocle | C9×C17⋊D17 | C2 |
| LCS | G ▷ C9×C172 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17^2,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^13,e^a=e^13,f^a=f^2,d^b=d^16,e^b=e^16660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 59);