Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22 |
| direct product | C3×#4549 |
| Sylow | C32 ⋊ C22⋊C16 |
170 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 170 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) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67522, C3×#67673, #11771342, … |
| maximal normal subgroup of | C3×#67522, C3×#67673, #11771342, … |
| maximal quotient of | C3×#67673, C3×#67709, C3×D4⋊(C3⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1175);