Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C3×C9×C4⋊C4 ⋊ C2 |
| Sylow | C3×C9 ⋊ #102 |
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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|b^2=c,d^2=e,f^3=h,b^a=bd,d^a=de,f^a=f^2h^2,g^a=g^2,h^a=h^2,d^b=de144 conjugacy classes — view the full character table.
| maximal subgroup of | #13137506, #13137508, #13137510, … |
| maximal normal subgroup of | #13137506, #13137508, #13137510, … |
| maximal quotient of | #13135731, #13135789, #13135792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 495);