Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#5062 |
| Fitting | C32×#124 ⋊ C2 |
| Sylow | C32 ⋊ #454 |
330 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67542, C3×#67460, #11772772, … |
| maximal normal subgroup of | C3×#67542, C3×#67460, #11772772, … |
| maximal quotient of | C3×#69702, C3×#69703, C3×#69704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4041);