Finite Group DatabasebetaFinite Group Databasebeta| order | 8862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D633 |
| unambiguous semidirect product | C3⋊(C7×D211) |
| Fitting, socle, Hall | C3×C7×C211 ⋊ C2 |
| derived, Hall | C3×C211 ⋊ C2×C7 |
| Hall | C7×C211 ⋊ D3 |
| Sylow | C211 ⋊ D3×C7 |
| Hall | C3×C7 ⋊ D211 |
| Sylow | C3 ⋊ C7×D211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D633 |
| commutator, hypocenter | C3×C211 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C211 | C2 |
| LCS | G ▷ C3×C211 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
2226 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×D211, D7×D633, D21⋊D211, … |
| maximal normal subgroup of | D3×C7×D211, D7×D633, D21⋊D211, … |
| maximal quotient of | C7×Dic633, C2×C7×D633, C7×D1899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8862, 12);