Finite Group DatabasebetaFinite Group Databasebeta| order | 7242 |
| automorphism | Aut(G) order 8111040 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3621 |
| unambiguous semidirect product | C3⋊D1207 |
| unambiguous semidirect product | C17⋊D213 |
| unambiguous semidirect product | C71⋊D51 |
| Fitting, socle, derived, Hall | C3×C17×C71 ⋊ C2 |
| Hall | C17×C71 ⋊ D3 |
| Hall | C3×C71 ⋊ D17 |
| Sylow | C71 ⋊ D51 |
| Hall | C3×C17 ⋊ D71 |
| Sylow | C17 ⋊ D213 |
| Sylow | C3 ⋊ D1207 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C71 | C2 |
| LCS | G ▷ C3×C17×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,71|b^a=b^2,c^a=c^16,d^a=d^701812 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D71, D17×D213, D3×D1207, … |
| maximal normal subgroup of | D51×D71, D17×D213, D3×D1207, … |
| maximal quotient of | Dic3621, C2×D3621, D10863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7242, 8);