Finite Group DatabasebetaFinite Group Databasebeta| order | 7282 |
| automorphism | Aut(G) order 12015300 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3641 |
| unambiguous semidirect product | C11⋊D331 |
| unambiguous semidirect product | C331⋊D11 |
| Fitting, socle, derived, Hall | C11×C331 ⋊ C2 |
| Sylow | C331 ⋊ D11 |
| Sylow | C11 ⋊ D331 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C331 | C2 |
| LCS | G ▷ C11×C331 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,331|b^a=b^10,c^a=c^3301822 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D331, C2×D3641, C3×D3641, … |
| maximal normal subgroup of | D11×D331, C2×D3641, C3×D3641, … |
| maximal quotient of | Dic3641, C2×D3641, C3×D3641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7282, 5);