Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #1010⋊C9 |
173 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^2,3^2,2^2,3,2|b^2=h,c^3=d,e^2=h,f^2=h,b^a=bh,g^a=g^2,e^c=ef,f^c=e,f^e=fh99 conjugacy classes — view the full character table.
| maximal subgroup of | #13146365, #13146366, #13146367, … |
| maximal normal subgroup of | #13146365, #13146366, #13146367, … |
| maximal quotient of | #5570⋊C9, D12×Q8⋊C9, #5572⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2402);