Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×Dic9⋊C8 |
| Sylow | C3×C9 ⋊ C4⋊C8 |
136 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #13138113, #13138114, #13138118, … |
| maximal normal subgroup of | #13138113, #13138114, #13138118, … |
| maximal quotient of | C3×#10588156, C3×#10588157, C3×Dic9⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 370);