Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×#103 |
| Fitting | C32×#103 ⋊ C2 |
| Sylow | C32 ⋊ C2×#103 |
486 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #103×#157, #11784041, #11786880, … |
| maximal normal subgroup of | #103×#157, #11784041, #11786880, … |
| maximal quotient of | C3⋊D3×Q8⋊C8, #11774384, #11774570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4382);