Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C33 ⋊ C22⋊Q8 |
548 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=de,c^a=cd,h^a=h^2,c^b=ce,f^b=f^2,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #13167879, #13167880, #13167913, … |
| maximal normal subgroup of | #13167879, #13167880, #13167913, … |
| maximal quotient of | #13159652, #13159658, #13159664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3458);