Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C25⋊#401 |
| Sylow | C25 ⋊ #401 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D25 |
| commutator, cosocle | C23×C25 | C23 |
| Frattini, socle, prime radical | C23×C5 | C22×D5 |
| Fitting | C25×#95 | C2 |
| hypercenter | #95 | D25 |
| hypocenter | C25 | #401 |
| LCS | G ▷ C23×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ #95 | |
177 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=f,b^2=d,c^2=e,g^5=h,b^a=be,c^a=cdf,g^a=g^4h^4,h^a=h^4,c^b=cef262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 290);