Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C32×#926 |
| Sylow | C33 ⋊ #117 |
672 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 294 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 | C3×#10589157, C3×#10589158, C3×#10589160, … |
| maximal normal subgroup of | C3×#10589157, C3×#10589158, C3×#10589160, … |
| maximal quotient of | C32×#4925, C32×#4926, C32×#4932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3762);