Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ #681 |
| Sylow | C5 ⋊ #3792 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,c^2=d,b^a=bd,e^a=f,f^a=e^2,g^a=g^4,e^c=e^2,f^c=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #13085525, #13085526, #13085597, … |
| maximal normal subgroup of | #13085525, #13085526, #13085597, … |
| maximal quotient of | #13086353, #13086356, C22⋊#67126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 580);