Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C3×C8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ #131 |
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 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|c^2=d,d^2=e,f^3=h,b^a=be,f^a=f^2h^2,g^a=g^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13135025, #13135039, #13135833, … |
| maximal normal subgroup of | #13135025, #13135039, #13135833, … |
| maximal quotient of | C8×#6226, #13143741, C8×C4⋊(C3⋊D9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1737);