Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×C5×C4⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ #2316 |
| Sylow | C5 ⋊ #82156 |
| Sylow | C3 ⋊ #10617102 |
1200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^2,i^a=i^2,c^b=ce,i^g=i^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 48545);