Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C9×C17 ⋊ D4 |
| Sylow | C17 ⋊ D36 |
| Sylow | C9 ⋊ C22⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×D17 |
| commutator, Fitting, cosocle | C2×C9×C17 | C22 |
| Frattini | C2×C3 | D3×D17 |
| socle | C2×C3×C17 | C2×D3 |
| hypocenter | C9×C17 | D4 |
| LCS | G ▷ C2×C9×C17 ▷ C9×C17 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 612 |
Polycyclic presentation:
2^3,3,17,3|a^2=c,d^3=f,b^a=bc,e^a=e^16,d^b=d^2f^2,f^b=f^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 10);