Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C5×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C22⋊C4 |
| Sylow | C9 ⋊ #685 |
| Sylow | C5 ⋊ (C2×D9)⋊C4 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|b^2=c,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 | #13084071, #13084079, #13084084, … |
| maximal normal subgroup of | #13084071, #13084079, #13084084, … |
| maximal quotient of | #13083848, #13083849, #13083852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 75);