Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C33 |
No aliases for this group.
| Fitting | C33×C22⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ C4×D4 |
1316 conjugacy classes of subgroups; only the 329 normal subgroups are shown.
This group has 1316 conjugacy classes of subgroups — too many to draw. Only its 329 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|c^2=d,b^a=be,f^a=f^2,g^a=g^2,h^a=h^2,c^b=ce150 conjugacy classes — view the full character table.
| maximal subgroup of | #13175444, #13175445, #13175449, … |
| maximal normal subgroup of | #13175444, #13175445, #13175449, … |
| maximal quotient of | #13163286, #13163290, #13163292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3889);