Finite Group DatabasebetaFinite Group Databasebeta| order | 8862 |
| automorphism | Aut(G) order 11166120 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4431 |
| unambiguous semidirect product | C3⋊D1477 |
| unambiguous semidirect product | C7⋊D633 |
| unambiguous semidirect product | C211⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C211 ⋊ C2 |
| Hall | C7×C211 ⋊ D3 |
| Hall | C3×C211 ⋊ D7 |
| Sylow | C211 ⋊ D21 |
| Hall | C3×C7 ⋊ D211 |
| Sylow | C7 ⋊ D633 |
| Sylow | C3 ⋊ D1477 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C211 | C2 |
| LCS | G ▷ C3×C7×C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,211|b^a=b^2,c^a=c^6,d^a=d^2102217 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D211, D7×D633, D3×D1477, … |
| maximal normal subgroup of | D21×D211, D7×D633, D3×D1477, … |
| maximal quotient of | Dic4431, C2×D4431, D13293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8862, 14);