Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | C5⋊D5 |
| commutator, hypocenter | C52 | C64 |
| Fitting, cosocle | C52×C32 | C2 |
| socle, prime radical | C2×C52 | C32 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
| 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^a=g^4,h^a=h^4448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1013);