Finite Group DatabasebetaFinite Group Databasebeta| order | 6468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64422⋊D11 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C22×C3 |
| Hall | D7×D77 ⋊ C3 |
| Hall | C11×#3862 ⋊ C22 |
| Hall | #3862 ⋊ C2×D11 |
| Sylow | C72 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ #64422⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C11 | C22×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,11|e^a=e^6,f^a=f^10,d^b=d^6,d^c=d^2,e^c=e^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6468, 77);