Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C33×C4 ⋊ Q8 |
| Sylow | C33 ⋊ C4⋊Q8 |
158 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 43 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=d,b^2=d,c^2=e,b^a=bd,f^a=g,g^a=f^2,h^a=h^2,c^b=ce,f^b=fg^2,g^b=f^2g^2,f^d=f^2,g^d=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | #13165762, #13165765, #13165768, … |
| maximal normal subgroup of | #13165762, #13165765, #13165768, … |
| maximal quotient of | #13167650, #13167651, #13167654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4331);