Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#11923883⋊C3) |
| unambiguous semidirect product | (C3⋊#11923883)⋊C3 |
| Fitting, socle, derived | C3×C172 ⋊ C3×C4 |
| Hall | C3×C172⋊C3 ⋊ C4 |
| Sylow | C172 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C172 | C3×C4 |
| prime radical | C3×(C17⋊D17)⋊C3 | C2 |
| cosocle | C3×C17⋊D17 | C2×C3 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,17^2|a^2=c,d^a=d^2,e^a=e^4,f^a=f^4,e^b=e^14f^4,f^b=e^11f^2,e^c=e^16,f^c=f^1690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 104);