Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C33×C4 |
No aliases for this group.
| Fitting | C2×C33×Q8 ⋊ C2 |
| Sylow | C33 ⋊ #124 |
1064 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=e,b^a=be,c^a=cd,f^a=f^2,g^a=g^2,h^a=h^2,c^b=ce144 conjugacy classes — view the full character table.
| maximal subgroup of | #13145686, #13146023, #13161235, … |
| maximal normal subgroup of | #13145686, #13146023, #13161235, … |
| maximal quotient of | #13163611, #13163622, #13163630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3955);