Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #19104513⋊C2 |
| unambiguous semidirect product | #19104514⋊C2 |
| derived, Hall | #14579583 ⋊ C22 |
| Sylow | C172 ⋊ C2×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #14579583 | C22 |
| Frattini | C3 | #13181892⋊C2 |
| Fitting, socle | C3×C172 | C2×D3 |
| LCS | G ▷ #14579583 | |
| UCS | C1 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17^2,3|c^3=f^2,c^a=c^2f,d^a=d^14e^5,e^a=d^12e^3,f^a=f^2,c^b=c^2f,d^b=d^3e^12,e^b=d^5e^14,f^b=f^2,d^c=d^14e^5,e^c=d^2e^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 47);