Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊(#1455⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C8 |
| unambiguous semidirect product | C5⋊(#1455⋊C3) |
| unambiguous semidirect product | #10598843⋊C3 |
| Fitting, derived | C5×C82 ⋊ C2×C3 |
| Hall | #10598843 ⋊ C3 |
| Sylow | C5 ⋊ #1455⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C82 | C2×C3 |
| Frattini | C42 | D5×A4 |
| socle | C22×C5 | C2×C42⋊C3 |
| LCS | G ▷ C5×C82 | |
| UCS | C1 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^2,5,2^4|c^2=g,d^2=fg,f^2=h,g^2=i,c^a=ci,d^a=dhi,e^a=e^4,c^b=dh,d^b=cdf,f^b=gh,g^b=fg,h^b=i,i^b=hi72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237241);