Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C25 |
| direct product | C2×C9×#235 |
| Fitting | C22×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#41 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13139422, #13139423, #13139447, … |
| maximal normal subgroup of | #13139422, #13139423, #13139447, … |
| maximal quotient of | C2×C4×C9×Dic6, C2×C9×#870, C9×#5470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2565);