Finite Group DatabasebetaFinite Group Databasebeta| order | 16473 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C19⋊(C172⋊C3) |
| unambiguous semidirect product | C172⋊(C19⋊C3) |
| Fitting, socle, derived, Hall | C172×C19 ⋊ C3 |
| Sylow | C172 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C172⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C19 | C3 |
| LCS | G ▷ C172×C19 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 969 |
Polycyclic presentation:
3,17^2,19|b^a=b^14c^12,c^a=b^15c^2,d^a=d^71833 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19⋊(C172⋊C3), #45681969, (C17⋊D17)⋊(C19⋊C3), … |
| maximal normal subgroup of | D19⋊(C172⋊C3), #45681969, (C17⋊D17)⋊(C19⋊C3), … |
| maximal quotient of | C2×C19⋊(C172⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16473, 4);