Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C5×#127 ⋊ C4 |
| Hall | C3×C5 ⋊ #1961 |
| Sylow | C5 ⋊ #71765 |
| Sylow | C3 ⋊ #10604617 |
824 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=dfg,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,i^a=i^3,c^b=cg,h^b=h^2,i^b=i^2,i^f=i^4102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 31663);