Finite Group DatabasebetaFinite Group Databasebeta| order | 16660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D85⋊D49 |
| unambiguous semidirect product | D245⋊D17 |
| unambiguous semidirect product | D833⋊D5 |
| Fitting, derived, Hall | C5×C17×C49 ⋊ C22 |
| Hall | C17×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ D5×D17 |
| Sylow | C17 ⋊ D5×D49 |
| Sylow | C5 ⋊ D17×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C17×C49 | C22 |
| Frattini | C7 | D35⋊D17 |
| socle | C5×C7×C17 | C2×D7 |
| LCS | G ▷ C5×C17×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4165 |
Polycyclic presentation:
2^2,5,7,17,7|d^7=f^6,d^a=d^6f,e^a=e^16,f^a=f^6,c^b=c^4,d^b=d^6f,f^b=f^61096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16660, 28);