Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C33 |
No aliases for this group.
| Fitting | C2×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ #135 |
868 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,h^a=h^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #13145579, #13145580, #13145585, … |
| maximal normal subgroup of | #13145579, #13145580, #13145585, … |
| maximal quotient of | #13163323, C4×#88851, C4×#88852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3912);