Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #100 |
264 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=e,b^a=bd,d^a=de,f^a=g,g^a=f^2,h^a=h^2,c^b=ce,f^c=f^2,g^c=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | #13154854, #13154856, #13154858, … |
| maximal normal subgroup of | #13154854, #13154856, #13154858, … |
| maximal quotient of | #13157219, #13157225, #13157227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3080);