Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C3×Dic3⋊C16 |
| unambiguous semidirect product | Dic3⋊(C3×C16) |
| Sylow | C32 ⋊ C4⋊C16 |
114 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×C4⋊C16, C2×C3×Dic3⋊C16, D3×Dic3⋊C16, … |
| maximal normal subgroup of | C3×D3×C4⋊C16, C2×C3×Dic3⋊C16, D3×Dic3⋊C16, … |
| maximal quotient of | C3×#67554, C3×#67555, C3×#67804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1127);