Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Hall | C3×C5 ⋊ #3458 |
| Sylow | C5 ⋊ #86571 |
| Sylow | C3 ⋊ #10618472 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#543 | C2 |
| prime radical | C24×C3×C5 | C23 |
| hypercenter | #543 | D15 |
| hypocenter | C3×C5 | #3458 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #543 | |
1992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^e=h^2,i^e=i^4198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 207498);