Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #64265⋊C3 |
148 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 25 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:
2^2,3^3,2^3|a^2=h,b^2=h,f^2=h,g^2=h,b^a=bh,d^a=d^2,e^a=e^2,f^a=gh,g^a=fh,d^c=de,f^d=g,g^d=fgh,g^f=gh49 conjugacy classes — view the full character table.
| maximal subgroup of | #13146384, #13146385, #13146389, … |
| maximal normal subgroup of | #13146384, #13146385, #13146389, … |
| maximal quotient of | #10593620⋊C3, #10593622⋊C3, C4⋊((C3⋊#226)⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2324);