Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×#101 |
| Fitting | C32×#101 ⋊ C2 |
| Sylow | C32 ⋊ C2×#101 |
311 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#355, D3×#4477, C3×D3×#356, … |
| maximal normal subgroup of | C3×D3×#355, D3×#4477, C3×D3×#356, … |
| maximal quotient of | C3×D3×#324, C3×#68125, C3×#68144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3729);