Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C4 |
| direct product | C24×C42⋊C3 |
| Fitting, Sylow | C24×C42 ⋊ C3 |
| derived | C42 ⋊ C24×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C42⋊C3 |
| commutator, cosocle, hypocenter | C42 | C24×C3 |
| Frattini | C22 | C24×A4 |
| Fitting | C24×C42 | C3 |
| socle | C26 | A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C24 | |
4340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084954);