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 ⋊ #3748 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,c^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 | #13084726, #13084727, #13084729, … |
| maximal normal subgroup of | #13084726, #13084727, #13084729, … |
| maximal quotient of | #13085086, C4⋊(C3⋊(C3⋊#168)), #13085113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 373);