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×C4⋊(C3⋊C16) |
| unambiguous semidirect product | C4⋊(C3×C3⋊C16) |
| Sylow | C32 ⋊ C4⋊C16 |
122 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 78 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×D4⋊(C3⋊C16), C3×#67503, #11771537, … |
| maximal normal subgroup of | C3×D4⋊(C3⋊C16), C3×#67503, #11771537, … |
| maximal quotient of | C3×#67439, C3×#67440, C3×#67657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1088);