Finite Group DatabasebetaFinite Group Databasebeta| order | 8218 |
| automorphism | Aut(G) order 14447244 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4109 |
| unambiguous semidirect product | C7⋊D587 |
| unambiguous semidirect product | C587⋊D7 |
| Fitting, socle, derived, Hall | C7×C587 ⋊ C2 |
| Sylow | C587 ⋊ D7 |
| Sylow | C7 ⋊ D587 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C587 | C2 |
| LCS | G ▷ C7×C587 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,587|b^a=b^6,c^a=c^5862056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D587, C2×D4109, C3×D4109, … |
| maximal normal subgroup of | D7×D587, C2×D4109, C3×D4109, … |
| maximal quotient of | Dic4109, C2×D4109, C3×D4109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8218, 3);