Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2×C17 |
| unambiguous semidirect product | C22⋊#14579583 |
| derived, Hall | C22×C172 ⋊ C9 |
| Sylow | C172 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ #14579583 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C172⋊C3) |
| commutator, hypocenter | C22×C172 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C172 | C3 |
| LCS | G ▷ C22×C172 | |
| UCS | C1 ◁ C3 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,17^2,3|a^3=f,b^a=c,c^a=bc,d^a=d^2e^12,e^a=d^15e^141164 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 67);