Finite Group DatabasebetaFinite Group Databasebeta| order | 6498 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C19⋊C3)⋊D19) |
| unambiguous semidirect product | (C19⋊C3)⋊D57 |
| Fitting, socle, derived | C3×C192 ⋊ C2×C3 |
| Hall | C3×C19×C19⋊C3 ⋊ C2 |
| Sylow | C192 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C192 | C2×C3 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,19^2|c^a=c^2,d^a=d^18,e^a=e^18,d^b=d^7261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6498, 82);