Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C17 |
| unambiguous semidirect product | C3⋊#16812402 |
| Fitting, socle | C3×C172 ⋊ Dic3 |
| derived, Hall | C3×C172⋊C3 ⋊ C4 |
| Sylow | C172 ⋊ C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C172⋊C3 | C4 |
| Fitting, socle | C3×C172 | Dic3 |
| prime radical, cosocle | C3×(C17⋊D17)⋊C3 | C2 |
| LCS | G ▷ C3×C172⋊C3 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^11f^11,f^a=e^9f^6,e^b=e^16,f^b=f^16,e^c=e^14f^4,f^c=e^11f^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 103);