Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C2×C32×C4×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ #685 |
| Sylow | C5 ⋊ #3752 |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3^2,5|b^2=c,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^4186 conjugacy classes — view the full character table.
| maximal subgroup of | #13086771, #13086779, #13086802, … |
| maximal normal subgroup of | #13086771, #13086779, #13086802, … |
| maximal quotient of | #13085088, #13085089, #13085092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 377);