Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23×C33 |
No aliases for this group.
| Sylow | C33 ⋊ #95 |
1064 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=d,b^a=be,f^a=f^2,g^a=g^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13145627, #13145629, #13145632, … |
| maximal normal subgroup of | #13145627, #13145629, #13145632, … |
| maximal quotient of | #13146069, #13146070, #13146072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2168);