Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | D12×#157 |
| Fitting | C33×C4 ⋊ C2×C4 |
| Sylow | C33 ⋊ C4×D4 |
328 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #13165041, #13165042, #13165256, … |
| maximal normal subgroup of | #13165041, #13165042, #13165256, … |
| maximal quotient of | #157×#204, #157×D24, #13166251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4225);