Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#63488 |
| Sylow | C3×C9 ⋊ #117 |
282 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #13135118, #13135126, #13135142, … |
| maximal normal subgroup of | #13135118, #13135126, #13135142, … |
| maximal quotient of | C3×#10588605, C3×#10588606, C3×#10588612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1544);