Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#834 |
| Sylow | C3×C9 ⋊ #99 |
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #13135179, #13135180, #13135181, … |
| maximal normal subgroup of | #13135179, #13135180, #13135181, … |
| maximal quotient of | C9×#4525, C9×#4526, C9×#4528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 453);