Finite Group DatabasebetaFinite Group Databasebeta| order | 17049 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5683⋊C3 |
| Fitting, socle, derived, Sylow | C5683 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5683 | C3 |
| LCS | G ▷ C5683 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
3,5683|b^a=b^45721897 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5683⋊C3, C2×C5683⋊C3 |
| maximal normal subgroup of | D5683⋊C3, C2×C5683⋊C3 |
| maximal quotient of | C2×C5683⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17049, 1);