Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×C5×D4 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×H(5,𝔽2) |
| Sylow | C5 ⋊ #85857 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×H(5,𝔽2) |
3320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^7,3,5|a^2=g,e^2=g,b^a=bf,d^a=df,h^a=h^2,i^a=i^3,c^b=cf,h^d=h^2,h^e=h^2,i^e=i^2,i^g=i^4129 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×H(5,𝔽2), #72229597, #72229650, … |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×H(5,𝔽2), #72229597, #72229650, … |
| maximal quotient of | #72260233, #72260263, #72260281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 204952);