Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C9⋊#11923880 |
| derived, Hall | C9×C172 ⋊ C4 |
| Sylow | C172 ⋊ Dic9 |
| Sylow | C9 ⋊ #11923880 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊(C17⋊D17) |
| commutator, hypocenter | C9×C172 | C4 |
| Frattini | C2×C3 | C3⋊(C17⋊D17) |
| Fitting, cosocle | C2×C9×C172 | C2 |
| socle, prime radical | C2×C3×C172 | D3 |
| LCS | G ▷ C9×C172 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17^2,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^16,d^a=d^16,f^a=f^22604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 41);