Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4×C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1044 |
| commutator, hypocenter | C52 | C4×C16 |
| Frattini | C2×C4 | C2×#1044 |
| Fitting | C2×C52×C8 | C4 |
| socle, prime radical | C22×C52 | C2×C8 |
| cosocle | C2×#6029 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,c^2=e,d^2=f,e^2=f,g^a=g^3,h^a=h^2,g^c=g^4,h^c=h^4160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2707);