Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#16812392 |
| derived, Hall | C3×C172⋊C3 ⋊ C4 |
| Sylow | C172 ⋊ C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#13181892 |
| commutator, hypocenter | C3×C172⋊C3 | C4 |
| Fitting, socle | C2×C3×C172 | D3 |
| prime radical, cosocle | C2×C3×C172⋊C3 | C2 |
| LCS | G ▷ C3×C172⋊C3 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,17^2,2|a^2=f,b^a=b^2,c^a=c^2,e^a=de^16,d^b=d^2e^12,e^b=d^15e^14348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 79);