Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of S42 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | S42 |
| unambiguous semidirect product | (A4×S4)⋊C2 |
| Fitting, socle | C24 ⋊ D32 |
| derived | A42 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A42 | C22 |
| Fitting, socle | C24 | D32 |
| LCS | G ▷ A42 | |
| UCS | C1 | |
274 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16 |
25 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8653);