Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D3×D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×D51 |
| Fitting, socle | C2×C32×C17 ⋊ C22 |
| derived, Hall | C32×C17 ⋊ C23 |
| Sylow | C17 ⋊ C2×D32 |
| Sylow | C32 ⋊ C22×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D51 |
| commutator, cosocle, hypocenter | C32×C17 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C17 | C22 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C2 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 204 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 156);