Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C4×C9×#67 |
| Fitting | C22×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C4×D4 |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #67×C9⋊C8, #13139522, #67⋊(C9⋊C8), … |
| maximal normal subgroup of | #67×C9⋊C8, #13139522, #67⋊(C9⋊C8), … |
| maximal quotient of | C4×C9×Dic3⋊C4, C9×#4933, C4×C9×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1555);