Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C33 |
No aliases for this group.
| Sylow | C33 ⋊ C22⋊Q8 |
1036 conjugacy classes of subgroups; only the 375 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 375 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=e,b^a=be,c^a=cd,f^a=f^2,g^a=g^2,h^a=h^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #13145636, #13145637, #13145998, … |
| maximal normal subgroup of | #13145636, #13145637, #13145998, … |
| maximal quotient of | #13163567, #13163571, #13163573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3932);