Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#4992 |
| Fitting | C2×C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #397 |
386 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71164, #11778443, C3×#71172, … |
| maximal normal subgroup of | C3×#71164, #11778443, C3×#71172, … |
| maximal quotient of | C3×#71570, C3×#69429, C3×#71567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3971);