Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C33 ⋊ C2×M16 |
382 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 91 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|b^2=d,d^2=e,f^a=f^2,h^a=h^2,c^b=ce,f^b=f^2,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #13154991, #13154993, #13154996, … |
| maximal normal subgroup of | #13154991, #13154993, #13154996, … |
| maximal quotient of | #13161475, #13161477, #13161478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3623);