Finite Group DatabasebetaFinite Group Databasebeta| order | 9894 |
| automorphism | Aut(G) order 15197184 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4947 |
| unambiguous semidirect product | C3⋊D1649 |
| unambiguous semidirect product | C17⋊D291 |
| unambiguous semidirect product | C97⋊D51 |
| Fitting, socle, derived, Hall | C3×C17×C97 ⋊ C2 |
| Hall | C17×C97 ⋊ D3 |
| Hall | C3×C97 ⋊ D17 |
| Sylow | C97 ⋊ D51 |
| Hall | C3×C17 ⋊ D97 |
| Sylow | C17 ⋊ D291 |
| Sylow | C3 ⋊ D1649 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C97 | C2 |
| LCS | G ▷ C3×C17×C97 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,97|b^a=b^2,c^a=c^16,d^a=d^962475 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D97, D17×D291, D3×D1649, … |
| maximal normal subgroup of | D51×D97, D17×D291, D3×D1649, … |
| maximal quotient of | Dic4947, C2×D4947, D14841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9894, 9);