Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #104 |
174 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 174 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) = 72 |
Polycyclic presentation:
2^5,3^3|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,g^a=g^2,h^a=h^2,f^b=f^2,h^b=h^2,g^f=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13137451, #13137452, #13138888, … |
| maximal normal subgroup of | #13137451, #13137452, #13138888, … |
| maximal quotient of | #13134967, #13134968, #13134973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 289);