Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of D153 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D153 |
| Fitting | C22×C9×C17 ⋊ C2 |
| derived, Hall | C9×C17 ⋊ C23 |
| Sylow | C17 ⋊ C22×D9 |
| Sylow | C9 ⋊ C22×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D153 |
| commutator, cosocle, hypocenter | C9×C17 | C23 |
| Frattini | C3 | C22×D51 |
| Fitting | C22×C9×C17 | C2 |
| socle | C22×C3×C17 | D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C22 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 612 |
312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 51);