Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C33 ⋊ #117 |
672 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 136 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:
2^5,3^3|a^2=d,b^2=d,c^2=e,b^a=be,h^a=h^2,f^b=f^2,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #13155301, #13155302, #13155438, … |
| maximal normal subgroup of | #13155301, #13155302, #13155438, … |
| maximal quotient of | #13158870, #13158871, #13158872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3419);