Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×#100 |
| Fitting | C32×#100 ⋊ C2 |
| Sylow | C32 ⋊ C2×#100 |
558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #11772559, #100×#157, #11786580, … |
| maximal normal subgroup of | #11772559, #100×#157, #11786580, … |
| maximal quotient of | C3⋊D3×#323, #11773803, #11773845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4325);