Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D153 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#3622 |
| derived, Hall | C9×C17 ⋊ C8 |
| Sylow | C17 ⋊ C9⋊C8 |
| Sylow | C9 ⋊ #3622 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D153 |
| commutator, hypocenter | C9×C17 | C8 |
| Frattini | C3×C4 | D51 |
| Fitting, cosocle | C4×C9×C17 | C2 |
| socle, prime radical | C2×C3×C17 | Dic3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1224 |
Polycyclic presentation:
2^3,3,17,3|a^2=b,b^2=c,d^3=f,d^a=d^2f^2,e^a=e^16,f^a=f^2312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 3);