Finite Group DatabasebetaFinite Group Databasebeta| order | 8226 |
| automorphism | Aut(G) order 11253168 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4113 |
| unambiguous semidirect product | C9⋊D457 |
| unambiguous semidirect product | C457⋊D9 |
| Fitting, derived, Hall | C9×C457 ⋊ C2 |
| Sylow | C457 ⋊ D9 |
| Sylow | C9 ⋊ D457 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C457 | C2 |
| Frattini | C3 | D1371 |
| socle | C3×C457 | D3 |
| LCS | G ▷ C9×C457 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,457,3|b^3=d^2,b^a=b^2d,c^a=c^456,d^a=d^22058 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D457, C2×D4113, D12339, … |
| maximal normal subgroup of | D9×D457, C2×D4113 |
| maximal quotient of | Dic4113, C2×D4113, D12339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8226, 6);