Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C33 ⋊ Q32 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=f^2g,h^a=h^2,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×#63736, #13165353, #13165354, … |
| maximal normal subgroup of | D3×#63736, #13165353, #13165354, … |
| maximal quotient of | #13155106, #13155112, C2×#11722790 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2757);