Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ D4×C22⋊C4 |
| Sylow | C5 ⋊ #76431 |
| Sylow | C3 ⋊ #10606609 |
2504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^a=be,c^a=cf,i^a=i^4,d^b=de,h^b=h^2,i^b=i^4,h^c=h^2,i^c=i^4,h^d=h^2174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 51667);