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 ⋊ #103 |
184 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=c,c^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,h^a=h^2,f^b=g,g^b=f^2,f^c=f^2,g^c=g^248 conjugacy classes — view the full character table.
| maximal subgroup of | #13165197, #13165198, #13165202, … |
| maximal normal subgroup of | #13165197, #13165198, #13165202, … |
| maximal quotient of | #13154771, #13154772, #13154779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2676);