Finite Group DatabasebetaFinite Group Databasebeta| order | 9506 |
| automorphism | Aut(G) order 19164096 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4753 |
| unambiguous semidirect product | C49⋊D97 |
| unambiguous semidirect product | C97⋊D49 |
| Fitting, derived, Hall | C49×C97 ⋊ C2 |
| Sylow | C97 ⋊ D49 |
| Sylow | C49 ⋊ D97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C97 | C2 |
| Frattini | C7 | D679 |
| socle | C7×C97 | D7 |
| LCS | G ▷ C49×C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,97,7|b^7=d^6,b^a=b^6d,c^a=c^96,d^a=d^62378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×D97, C2×D4753, C3×D4753, … |
| maximal normal subgroup of | D49×D97, C2×D4753, C3×D4753, … |
| maximal quotient of | Dic4753, C2×D4753, C3×D4753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9506, 4);