Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C26 |
| direct product | C22×C9×#67 |
| Fitting | C24×C3×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22×D4 |
842 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11720332, #13141098, #13141133, … |
| maximal normal subgroup of | C2×#11720332, #13141098, #13141133, … |
| maximal quotient of | C22×C9×Dic3⋊C4, C2×C9×#924, C22×C9×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2613);