Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#4876 |
| Sylow | C32 ⋊ #501 |
198 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 86 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×D3×#501, C2×C3×#4876, D3×#4876, … |
| maximal normal subgroup of | C3×D3×#501, C2×C3×#4876, D3×#4876, … |
| maximal quotient of | C3×#70608, C3×#68860, C3×#70613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3855);