Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C3×#875 |
| Fitting | C2×C32×C42 ⋊ C2 |
| Sylow | C32 ⋊ C2×#124 |
714 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70784, C3×#70828, #11774033, … |
| maximal normal subgroup of | C3×#70784, C3×#70828, #11774033, … |
| maximal quotient of | C2×C3×#4936, C2×C3×#4940, C2×C3×#4939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7455);