Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C17 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C172 ⋊ C4 |
| Sylow | C172 ⋊ #157 |
| Sylow | C32 ⋊ #11923880 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C172 | C4 |
| prime radical, cosocle | C172×C3⋊D3 | C2 |
| LCS | G ▷ C32×C172 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|a^2=b,c^a=cd,d^a=cd^2,e^a=e^16,f^a=f^16,c^b=c^2,d^b=d^2870 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 148);