Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #108 |
125 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 125 conjugacy classes of subgroups — too many to draw. Only its 40 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=d,b^2=c,c^2=e,d^2=e,b^a=bd,g^a=g^2,h^a=h^2,d^b=de,f^b=f^2,h^b=h^2,g^f=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13137443, #13137444, #13138886, … |
| maximal normal subgroup of | #13137443, #13137444, #13138886, … |
| maximal quotient of | #13134969, #13134970, #13135176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 286);