Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C216 |
| direct product | C26×A4 |
| Fitting, socle, Sylow | C28 ⋊ C3 |
| derived | C22 ⋊ C26×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | A4 |
| commutator, cosocle, hypocenter | C22 | C26×C3 |
| Frattini | C1 | G |
| Fitting, socle | C28 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C26 | |
148483 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C24×A42, C22×A4×#120, C24×GL(2,ℤ/4), … |
| maximal normal subgroup of | C24×A42, C22×A4×#120, C24×GL(2,ℤ/4), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085322);