Finite Group DatabasebetaFinite Group Databasebeta| order | 17298 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C312 · Schur multiplier (H2) = C31 |
| direct product | D9×C312 |
| unambiguous semidirect product | C9⋊(C2×C312) |
| Fitting, Hall | C9×C312 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C312 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C312 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C312 |
| Frattini | C3 | D3×C312 |
| Fitting | C9×C312 | C2 |
| socle | C3×C312 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C312 | |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8649 |
5766 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C31×D31, D9×C31⋊D31, C2×D9×C312 |
| maximal normal subgroup of | D9×C31×D31, D9×C31⋊D31, C2×D9×C312 |
| maximal quotient of | C312×Dic9, C2×D9×C312 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17298, 31);