Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C33 ⋊ #104 |
190 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 190 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) = 24 |
Polycyclic presentation:
2^5,3^3|b^2=cd,c^2=e,b^a=bc,c^a=ce,d^a=de,f^a=f^2,g^a=f^2g,h^a=h^2,c^b=ce,d^b=de,f^b=f^2g^2,g^b=f^2g,f^c=f^2,g^c=g^245 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63741, #13165476, #13165477, … |
| maximal normal subgroup of | D3×#63741, #13165476, #13165477, … |
| maximal quotient of | #13155074, #13155076, #13155079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2762);