Finite Group DatabasebetaFinite Group Databasebeta| order | 8382 |
| automorphism | Aut(G) order 10561320 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4191 |
| unambiguous semidirect product | C3⋊D1397 |
| unambiguous semidirect product | C11⋊D381 |
| unambiguous semidirect product | C127⋊D33 |
| Fitting, socle, derived, Hall | C3×C11×C127 ⋊ C2 |
| Hall | C11×C127 ⋊ D3 |
| Hall | C3×C127 ⋊ D11 |
| Sylow | C127 ⋊ D33 |
| Hall | C3×C11 ⋊ D127 |
| Sylow | C11 ⋊ D381 |
| Sylow | C3 ⋊ D1397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C127 | C2 |
| LCS | G ▷ C3×C11×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,127|b^a=b^2,c^a=c^10,d^a=d^1262097 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D127, D11×D381, D3×D1397, … |
| maximal normal subgroup of | D33×D127, D11×D381, D3×D1397, … |
| maximal quotient of | Dic4191, C2×D4191, D12573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8382, 9);