Finite Group DatabasebetaFinite Group Databasebeta| order | 16762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C17⋊D493 |
| unambiguous semidirect product | C29⋊(C17⋊D17) |
| Fitting, socle, derived, Hall | C172×C29 ⋊ C2 |
| Sylow | C172 ⋊ D29 |
| Sylow | C29 ⋊ C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C29 | C2 |
| LCS | G ▷ C172×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8381 |
Polycyclic presentation:
2,17^2,29|b^a=b^16,c^a=c^16,d^a=d^284192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D493, D29×C17⋊D17, #45692854, … |
| maximal normal subgroup of | D17×D493, D29×C17⋊D17, #45692854, … |
| maximal quotient of | #45692831, C2×C17⋊D493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16762, 6);