Finite Group DatabasebetaFinite Group Databasebeta| order | 8874 |
| automorphism | Aut(G) order 11926656 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4437 |
| unambiguous semidirect product | C9⋊D493 |
| unambiguous semidirect product | C17⋊D261 |
| unambiguous semidirect product | C29⋊D153 |
| Fitting, derived, Hall | C9×C17×C29 ⋊ C2 |
| Hall | C17×C29 ⋊ D9 |
| Hall | C9×C29 ⋊ D17 |
| Hall | C9×C17 ⋊ D29 |
| Sylow | C29 ⋊ D153 |
| Sylow | C17 ⋊ D261 |
| Sylow | C9 ⋊ D493 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C17×C29 | C2 |
| Frattini | C3 | D1479 |
| socle | C3×C17×C29 | D3 |
| LCS | G ▷ C9×C17×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,29,3|b^3=e^2,b^a=b^2e,c^a=c^16,d^a=d^28,e^a=e^22220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D153, D17×D261, D9×D493, … |
| maximal normal subgroup of | D29×D153, D17×D261, D9×D493, … |
| maximal quotient of | Dic4437, C2×D4437, D13311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8874, 8);