Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C9 ⋊ M16 |
| Sylow | C9 ⋊ #681 |
| Sylow | C5 ⋊ #3667 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|a^2=c,c^2=d,e^3=g,b^a=bd,e^a=e^2g^2,f^a=f^4,g^a=g^2186 conjugacy classes — view the full character table.
| maximal subgroup of | #13083711, #13083731, #13083737, … |
| maximal normal subgroup of | #13083711, #13083731, #13083737, … |
| maximal quotient of | #13083846, C4⋊(C9⋊#168), #13083873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 71);