Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#63447 |
| Fitting | C2×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ C2×#124 |
495 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11774014, C4×#63447, #11802330, … |
| maximal normal subgroup of | #11774014, C4×#63447, #11802330, … |
| maximal quotient of | C2×#10588330, C2×#10588624, C2×#10588349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1475);