Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3×C9 ⋊ C4×D4 |
308 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|b^2=d,c^2=d,f^3=h,c^a=cde,g^a=g^2,f^b=f^2h^2,h^b=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #13147477, #13147506, C4×#88638, … |
| maximal normal subgroup of | #13147477, #13147506, C4×#88638, … |
| maximal quotient of | #13137709, #13137711, #13137719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 979);