Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C210 |
| direct product | C22×C22⋊(C22⋊A4) |
| Fitting, socle, Sylow | C28 ⋊ C3 |
| derived | C26 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C26 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C28 | C3 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C22 | |
139433 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085320);