Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#912 |
| Fitting | C2×C32×D8 ⋊ C2 |
| Sylow | C32 ⋊ C2×#135 |
570 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69188, #11796652, C3×#69189, … |
| maximal normal subgroup of | C3×#69188, #11796652, C3×#69189, … |
| maximal quotient of | C2×C3×#4772, C2×C3×#4880, C2×C3×Dic3×D8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7735);