Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C27 ⋊ C2 |
| Sylow | C27 ⋊ #117 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=d,f^3=g,g^3=h,c^a=ce,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13134196, #13134197, #13134215, … |
| maximal normal subgroup of | #13134196, #13134197, #13134215, … |
| maximal quotient of | #13134152, #13134156, #13134158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 88);