Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C4 |
| direct product | C3×#5082 |
| Sylow | C32 ⋊ #491 |
214 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67551, #11772888, C3×#71246, … |
| maximal normal subgroup of | C3×#67551, #11772888, C3×#71246, … |
| maximal quotient of | C3×#69575, C3×#69675, C3×#71786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4061);