Finite Group DatabasebetaFinite Group Databasebeta| order | 16762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D493 |
| unambiguous semidirect product | C17⋊(C17×D29) |
| unambiguous semidirect product | C29⋊(C17×D17) |
| Fitting, socle, Hall | C172×C29 ⋊ C2 |
| derived | C17×C29 ⋊ C2×C17 |
| Sylow | C172 ⋊ D29 |
| Sylow | C29 ⋊ C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D493 |
| commutator, cosocle, hypocenter | C17×C29 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C172×C29 | C2 |
| LCS | G ▷ C17×C29 | |
| UCS | C1 ◁ C17 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 986 |
4216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D17×D29, C17×#14520308, C17×#14520307, … |
| maximal normal subgroup of | C17×D17×D29, C17×#14520308, C17×#14520307, … |
| maximal quotient of | C17×Dic493, C2×C17×D493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16762, 8);