Finite Group DatabasebetaFinite Group Databasebeta| order | 918 |
| isoclinism | isoclinic class of C3⋊D153 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D153 |
| unambiguous semidirect product | C9⋊D51 |
| unambiguous semidirect product | C17⋊(C3⋊D9) |
| Fitting, derived, Hall | C3×C9×C17 ⋊ C2 |
| Sylow | C3×C9 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C9×C17 | C2 |
| Frattini | C3 | C3⋊D51 |
| socle | C32×C17 | D3 |
| LCS | G ▷ C3×C9×C17 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 459 |
Polycyclic presentation:
2,3^2,17,3|b^3=e,b^a=b^2e^2,c^a=c^2,d^a=d^16,e^a=e^2231 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C3⋊D9, D3×D153, D9×D51, … |
| maximal normal subgroup of | D17×C3⋊D9, D3×D153, D9×D51, … |
| maximal quotient of | C3⋊Dic153, C2×C3⋊D153 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(918, 18);