Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊(C3⋊Dic15) |
| Hall | C32×C5 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C4⋊Dic5 |
| Sylow | C5 ⋊ C4⋊(C3⋊Dic3) |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,b^2=d,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 | #13084733, #13084735, #13084739, … |
| maximal normal subgroup of | #13084733, #13084735, #13084739, … |
| maximal quotient of | C4⋊(C3⋊(C3⋊#168)), #13085099, #13085100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 376);