Finite Group DatabasebetaFinite Group Databasebeta| order | 8862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D211⋊C3)⋊C7 |
| unambiguous semidirect product | (D211⋊C7)⋊C3 |
| unambiguous semidirect product | ((C211⋊C3)⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C211 ⋊ C2×C3×C7 |
| Hall | (C211⋊C3)⋊C7 ⋊ C2 |
| Hall | D211⋊C7 ⋊ C3 |
| Hall | C211⋊C7 ⋊ C2×C3 |
| Hall | D211⋊C3 ⋊ C7 |
| Hall | C211⋊C3 ⋊ C2×C7 |
| Hall | D211 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C211 | C2×C3×C7 |
| LCS | G ▷ C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,211|d^a=d^210,d^b=d^196,d^c=d^17147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8862, 30);