Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #67194 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C32 |
| Sylow | C32 ⋊ #3926 |
| Sylow | C5 ⋊ #63725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #67194 |
| commutator, hypocenter | C32×C5 | C32 |
| Fitting | C32×C4×C5 | C8 |
| socle, prime radical | C2×C32×C5 | C16 |
| cosocle | C5×#3708 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3^2,5|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2g^2,g^a=f^2,h^a=h^4,f^b=f^2g,g^b=fg,f^c=f^2,g^c=g^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1695);