Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C33 ⋊ C8 |
| Sylow | C33 ⋊ C22⋊C8 |
142 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=e,b^a=bd,f^a=f^2g^2,g^a=fg^2,h^a=h^2,f^c=g^2,g^c=f,f^e=f^2,g^e=g^248 conjugacy classes — view the full character table.
| maximal subgroup of | #13165059, #13165060, #13165099, … |
| maximal normal subgroup of | #13165059, #13165060, #13165099, … |
| maximal quotient of | #13166214, #13166217, #13166220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4210);