Finite Group DatabasebetaFinite Group Databasebeta| order | 8946 |
| automorphism | Aut(G) order 11271960 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4473 |
| unambiguous semidirect product | C7⋊D639 |
| unambiguous semidirect product | C9⋊D497 |
| unambiguous semidirect product | C71⋊D63 |
| Fitting, derived, Hall | C7×C9×C71 ⋊ C2 |
| Hall | C9×C71 ⋊ D7 |
| Hall | C7×C71 ⋊ D9 |
| Sylow | C71 ⋊ D63 |
| Hall | C7×C9 ⋊ D71 |
| Sylow | C9 ⋊ D497 |
| Sylow | C7 ⋊ D639 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C9×C71 | C2 |
| Frattini | C3 | D1491 |
| socle | C3×C7×C71 | D3 |
| LCS | G ▷ C7×C9×C71 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,71,3|b^3=e^2,b^a=b^2e,c^a=c^6,d^a=d^70,e^a=e^22238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D63×D71, D7×D639, D9×D497, … |
| maximal normal subgroup of | D63×D71, D7×D639, D9×D497, … |
| maximal quotient of | Dic4473, C2×D4473, D13419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8946, 10);