Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C3×C5×#121 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×D42 |
| Sylow | C5 ⋊ D3×D42 |
| Sylow | C3 ⋊ D42×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×#121 | C22 |
| hypercenter | #121 | D3×D5 |
| hypocenter | C3×C5 | C2×D42 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #121 | |
5072 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|b^a=bf,c^a=cg,d^b=df,h^b=h^2,h^d=h^2,h^e=h^2,i^e=i^4153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 208123);