Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#5185 |
| Fitting | C2×C32×Q16 ⋊ C2 |
| Sylow | C32 ⋊ #464 |
254 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#464, C2×C3×#5185, D3×#5185, … |
| maximal normal subgroup of | C3×D3×#464, C2×C3×#5185, D3×#5185, … |
| maximal quotient of | C3×#71150, C3×#71054, C3×#71055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4164);