Finite Group DatabasebetaFinite Group Databasebeta| order | 8330 |
| automorphism | Aut(G) order 11195520 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4165 |
| unambiguous semidirect product | C5⋊D833 |
| unambiguous semidirect product | C17⋊D245 |
| unambiguous semidirect product | C49⋊D85 |
| Fitting, derived, Hall | C5×C17×C49 ⋊ C2 |
| Hall | C17×C49 ⋊ D5 |
| Hall | C5×C49 ⋊ D17 |
| Hall | C5×C17 ⋊ D49 |
| Sylow | C49 ⋊ D85 |
| Sylow | C17 ⋊ D245 |
| Sylow | C5 ⋊ D833 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C17×C49 | C2 |
| Frattini | C7 | D595 |
| socle | C5×C7×C17 | D7 |
| LCS | G ▷ C5×C17×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,17,7|c^7=e^6,b^a=b^4,c^a=c^6e,d^a=d^16,e^a=e^62084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D245, D49×D85, D5×D833, … |
| maximal normal subgroup of | D17×D245, D49×D85, D5×D833, … |
| maximal quotient of | Dic4165, C2×D4165, C3×D4165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8330, 8);