Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#809 |
| Fitting | C3×C9×C4⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ #102 |
176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | #13137621, #13137623, #13137637, … |
| maximal normal subgroup of | #13137621, #13137623, #13137637, … |
| maximal quotient of | C9×#4451, C9×#4483, C9×#4485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 354);