Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C172 ⋊ C22 |
| Sylow | C172 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ D172 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C172 | C22 |
| LCS | G ▷ C32×C172 | |
| UCS | C1 | |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|c^a=c^2,d^a=d^2,e^a=e^16,e^b=e^16,f^b=f^16684 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 134);