Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C2×C36 |
| direct product | C2×C33×A4 |
| unambiguous semidirect product | C23⋊C34 |
| unambiguous semidirect product | (C23×C3)⋊C33 |
| Fitting, socle | C23×C33 ⋊ C3 |
| derived | C22 ⋊ C2×C34 |
| Sylow | C23 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C33 | A4 |
| commutator, cosocle, hypocenter | C22 | C2×C34 |
| Frattini | C1 | G |
| Fitting, socle | C23×C33 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C33 | |
960 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 752);