Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #10624311 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C32×C5 ⋊ #103 |
| Sylow | C32 ⋊ #3942 |
| Sylow | C5 ⋊ PSU(3,𝔽2)⋊C4 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=d,c^2=e,b^a=bcde,f^a=f^2g^2,g^a=f^2,h^a=h^4,c^b=ce,f^b=f^2g,f^c=f^2g,g^c=fg,f^e=f^2,g^e=g^254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4711);