Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×M16 |
| unambiguous semidirect product | (C22×M16)⋊C32 |
| unambiguous semidirect product | (C22×C3×M16)⋊C3 |
| Fitting | C22×C3×M16 ⋊ C3 |
| Sylow | C22×M16 ⋊ C32 |
206 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×#100, C3×A4×#101, C3×A4×#104, … |
| maximal normal subgroup of | C3×A4×#100, C3×A4×#101, C3×A4×#104, … |
| maximal quotient of | C3×A4×#97, C3×A4×C22⋊C8, C3×A4×C4⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7431);