Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C5×Q8 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ #2368 |
| Sylow | C5 ⋊ #76616 |
| Sylow | C3 ⋊ #10617287 |
1096 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=fg,c^2=ef,b^a=be,c^a=cf,i^a=i^3,d^b=de,i^b=i^2,h^c=h^2,h^d=h^2,i^g=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 55517);