Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4⋊Dic9 |
| Sylow | C3×C9 ⋊ C2×C4⋊C4 |
330 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 184 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 | #13135123, #13135138, #13135140, … |
| maximal normal subgroup of | #13135123, #13135138, #13135140, … |
| maximal quotient of | C2×C3×C4⋊(C9⋊C8), C3×#10588604, C3×C4×C4⋊Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1543);