Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C23×C33 |
| direct product | C22×C33×D3 |
| unambiguous semidirect product | C3⋊(C23×C33) |
| unambiguous semidirect product | (C2×C3)⋊(C22×C33) |
| Fitting, socle | C22×C34 ⋊ C2 |
| derived | C3 ⋊ C23×C33 |
| Sylow | C34 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C33 | D3 |
| commutator, cosocle, hypocenter | C3 | C23×C33 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C33 | |
1286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 753);