Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C27 ⋊ #126 |
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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=d,f^3=g,g^3=h,c^a=cde,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=ce144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720128, #13136232, #13136233, … |
| maximal normal subgroup of | C2×#11720128, #13136232, #13136233, … |
| maximal quotient of | #13134158, #13134159, #13134160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 95);