Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #99 |
260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^5,3^3|a^2=c,f^3=h,b^a=bd,d^a=de,f^a=f^2h^2,g^a=g^2,h^a=h^2,c^b=ce141 conjugacy classes — view the full character table.
| maximal subgroup of | #13135183, #13135185, #13135187, … |
| maximal normal subgroup of | #13135183, #13135185, #13135187, … |
| maximal quotient of | #13135878, #13135880, #13135884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 544);