Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #19104522⋊C2 |
| unambiguous semidirect product | #19104523⋊C2 |
| Fitting, socle, Sylow | C172 ⋊ C2×D9 |
| derived, Hall | #14579585 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #14579585 | C22 |
| Fitting, socle | C172 | C2×D9 |
| LCS | G ▷ #14579585 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|c^3=d,c^a=c^2d^2,d^a=d^2,e^a=ef^11,f^a=f^16,c^b=c^2d^2,d^b=d^2,e^b=e^16f^6,e^c=e^12f^6,f^c=e^16f,e^d=e^14f^5,f^d=e^2f^244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 92);