Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#63391 |
| Sylow | C3×C9 ⋊ #100 |
192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | #13135180, #13135182, #13135192, … |
| maximal normal subgroup of | #13135180, #13135182, #13135192, … |
| maximal quotient of | C3×#10588202, C3×#10588207, C3×#10588217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 448);