Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#5073 |
| Fitting | C32×#127 ⋊ C2 |
| Sylow | C32 ⋊ #493 |
378 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67541, #11772833, C3×#71015, … |
| maximal normal subgroup of | C3×#67541, #11772833, C3×#71015, … |
| maximal quotient of | C3×#71255, C3×#71275, C3×#71297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4052);