Finite Group DatabasebetaFinite Group Databasebeta| order | 17986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C17⋊(C23⋊D23) |
| unambiguous semidirect product | C23⋊D391 |
| Fitting, socle, derived, Hall | C17×C232 ⋊ C2 |
| Sylow | C232 ⋊ D17 |
| Sylow | C17 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C232 | C2 |
| LCS | G ▷ C17×C232 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8993 |
Polycyclic presentation:
2,17,23^2|b^a=b^16,c^a=c^22,d^a=d^224498 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49112618, D23×D391, D17×C23⋊D23, … |
| maximal normal subgroup of | #49112618, D23×D391, D17×C23⋊D23, … |
| maximal quotient of | C23⋊Dic391, C2×C17⋊(C23⋊D23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17986, 6);