Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×Q16 |
| unambiguous semidirect product | (C22×Q16)⋊C32 |
| unambiguous semidirect product | (C22×C3×Q16)⋊C3 |
| Fitting | C22×C3×Q16 ⋊ C3 |
| Sylow | C22×Q16 ⋊ C32 |
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×SD32, C3×A4×Q32, C2×C3×A4×Q16, … |
| maximal normal subgroup of | C3×A4×SD32, C3×A4×Q32, C2×C3×A4×Q16, … |
| maximal quotient of | C3×A4×#103, C3×A4×#107, C3×#3363⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7436);