Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#4836 |
| Fitting | C32×C4⋊C8 ⋊ C2 |
| Sylow | C32 ⋊ #435 |
267 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 267 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×#435, C2×C3×#4836, D3×#4836, … |
| maximal normal subgroup of | C3×D3×#435, C2×C3×#4836, D3×#4836, … |
| maximal quotient of | C3×#68559, C3×#68519, C3×#68520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3815);