Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C33 ⋊ C2×Q16 |
512 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 84 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=e,b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,h^a=h^2,c^b=cd,d^b=de,f^b=f^2,g^b=g^2,d^c=de69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63944, #13171642, #13171668, … |
| maximal normal subgroup of | D3×#63944, #13171642, #13171668, … |
| maximal quotient of | #13159085, #13159141, #13159143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3544);