Finite Group DatabasebetaFinite Group Databasebeta| order | 8382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D127⋊C3) |
| unambiguous semidirect product | (C127⋊C3)⋊D11 |
| unambiguous semidirect product | D1397⋊C3 |
| Fitting, socle, derived, Hall | C11×C127 ⋊ C2×C3 |
| Hall | C11×C127⋊C3 ⋊ C2 |
| Hall | D1397 ⋊ C3 |
| Hall | C127⋊C3 ⋊ D11 |
| Sylow | C127 ⋊ C3×D11 |
| Sylow | C11 ⋊ D127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C127 | C2×C3 |
| LCS | G ▷ C11×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,127|c^a=c^10,d^a=d^126,d^b=d^107252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8382, 12);