Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C33 ⋊ C4×D4 |
700 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=e,c^2=d,b^a=be,c^a=ce,h^a=h^2,f^b=f^2,g^b=g^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #13166457, #13166458, #13166480, … |
| maximal normal subgroup of | #13166457, #13166458, #13166480, … |
| maximal quotient of | #13159359, #13159360, #13159377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3479);