Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C17 |
| unambiguous semidirect product | C3⋊(C3⋊#11923880) |
| derived, Hall | C32×C172 ⋊ C4 |
| Sylow | C172 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ #11923880 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊(C17⋊D17)) |
| commutator, hypocenter | C32×C172 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C172 | C2 |
| LCS | G ▷ C32×C172 | |
| UCS | C1 ◁ C2 | |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,17^2,2|a^2=f,b^a=b^2,c^a=c^2,d^a=d^16,e^a=e^162604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 90);