Finite Group DatabasebetaFinite Group Databasebeta| order | 6498 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#14524212 |
| Fitting, socle | C3×C192 ⋊ D3 |
| derived, Hall | C3×#11762246 ⋊ C2 |
| Sylow | C192 ⋊ C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×#11762246 | C2 |
| Fitting, socle | C3×C192 | D3 |
| LCS | G ▷ C3×#11762246 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,19^2|b^a=b^2,c^a=c^2,d^a=e,e^a=d,d^b=d^11,e^b=e^7213 conjugacy classes — view the full character table.
| maximal subgroup of | #14524212⋊D3, #27188880, D3×#14524212, … |
| maximal normal subgroup of | #14524212⋊D3, #27188880, D3×#14524212, … |
| maximal quotient of | C3⋊#16864564, C2×C3⋊#14524212, C5×C3⋊#14524212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6498, 86);