Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ #2380 |
| Sylow | C5 ⋊ #74298 |
| Sylow | C3 ⋊ #10617370 |
1296 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,i^a=i^2,c^b=cef,d^b=de,h^b=h^2,i^g=i^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 56926);