Finite Group DatabasebetaFinite Group Databasebeta| order | 8628 |
| automorphism | Aut(G) order 6194904 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4314 |
| direct product | C2×D2157 |
| unambiguous semidirect product | (C2×C3)⋊D719 |
| unambiguous semidirect product | (C2×C719)⋊D3 |
| Fitting, socle | C2×C3×C719 ⋊ C2 |
| derived, Hall | C3×C719 ⋊ C22 |
| Sylow | C719 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D719 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2157 |
| commutator, hypocenter | C3×C719 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C719 | C2 |
| LCS | G ▷ C3×C719 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6471, D3×D2157, C2×C3×D2157, … |
| maximal normal subgroup of | C2×C3×D2157, D8628 |
| maximal quotient of | C2×D6471, D3×D2157, C2×C3×D2157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8628, 8);