Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#3663 |
| Fitting | C2×C3×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×M16 |
226 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 104 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 | #13135036, C3×#10588191, Dic3×#3663, … |
| maximal normal subgroup of | #13135036, C3×#10588191, Dic3×#3663, … |
| maximal quotient of | C3×#10588359, C3×#10588367, C3×C4×#3663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1454);