Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1312 |
| Sylow | C5 ⋊ #67499 |
| Sylow | C3 ⋊ #10597929 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4×C8 | D3×D5 |
| commutator | C2×C3×C5 | C4×C16 |
| Fitting, cosocle | C3×C4×C5×C8 | C22 |
| socle, prime radical | C22×C3×C5 | C4×C8 |
| hypocenter | C3×C5 | #1312 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4×C8 | |
184 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^2,i^b=i^4336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 3176);