Finite Group DatabasebetaFinite Group Databasebeta| order | 6468 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C11⋊#10596875 |
| derived, Hall | C72×C11 ⋊ C3×C4 |
| Hall | C7⋊Dic77 ⋊ C3 |
| Hall | C11×#3862 ⋊ C4 |
| Hall | #3862 ⋊ Dic11 |
| Sylow | C72 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ #10596875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#64425 |
| commutator, hypocenter | C72×C11 | C3×C4 |
| Fitting, socle | C2×C72×C11 | C2×C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,11,2|a^2=f,c^a=c^6,d^a=d^6,e^a=e^10,c^b=c^2,d^b=d^4218 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6468, 42);