Finite Group DatabasebetaFinite Group Databasebeta| order | 6498 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#14524208 |
| Fitting, socle, derived | C3×C192 ⋊ C2×C3 |
| Hall | C3×#11762245 ⋊ 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 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,19^2|c^a=c^2,d^a=d^18,d^b=d^7,e^b=e^7198 conjugacy classes — view the full character table.
| maximal subgroup of | #14524208⋊D3, #27188869, D3×#14524208, … |
| maximal normal subgroup of | #14524208⋊D3, #27188869, D3×#14524208, … |
| maximal quotient of | C3⋊#16864560, C2×C3⋊#14524208, C5×C3⋊#14524208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6498, 80);