Finite Group DatabasebetaFinite Group Databasebeta| order | 10668 |
| automorphism | Aut(G) order 8065008 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5334 |
| direct product | C2×D2667 |
| unambiguous semidirect product | (C2×C3)⋊D889 |
| unambiguous semidirect product | (C2×C7)⋊D381 |
| unambiguous semidirect product | (C2×C127)⋊D21 |
| Fitting, socle | C2×C3×C7×C127 ⋊ C2 |
| derived, Hall | C3×C7×C127 ⋊ C22 |
| Hall | C7×C127 ⋊ C2×D3 |
| Hall | C3×C127 ⋊ C2×D7 |
| Sylow | C127 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D127 |
| Sylow | C7 ⋊ C2×D381 |
| Sylow | C3 ⋊ C2×D889 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2667 |
| commutator, cosocle, hypocenter | C3×C7×C127 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C127 | C2 |
| LCS | G ▷ C3×C7×C127 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2670 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10668, 73);