Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | #10619439⋊C3 |
| Fitting | C2×C5×2−1+4 ⋊ C2×C3 |
| Hall | #10619439 ⋊ C3 |
| Sylow | C5 ⋊ #87537 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Fitting | C2×C5×2−1+4 | C2×C3 |
| socle | C2×C5 | C24×A4 |
| hypercenter | C2×D4 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
2432 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 2432 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^4,3,2^2,5,2|f^2=i,g^2=i,d^a=di,h^a=h^4,c^b=ci,f^e=fg,g^e=f,g^f=gi143 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240366);