Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#4828 |
| Sylow | C32 ⋊ #446 |
207 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 207 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) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#446, C2×C3×#4828, D3×#4828, … |
| maximal normal subgroup of | C3×D3×#446, C2×C3×#4828, D3×#4828, … |
| maximal quotient of | C3×#68652, C3×#68654, C3×#70467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3807);