Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C25 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #1035 |
| commutator, hypocenter | C25 | C64 |
| Frattini | C5×C16 | AGL(1,𝔽5) |
| Fitting | C16×C25 | C4 |
| socle, prime radical | C2×C5 | #3928 |
| cosocle | #11716342 | C2 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C16 | |
21 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^5=h,g^a=g^2h,h^a=h^2,g^b=g^4h^4,h^b=h^4160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3);