Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6053⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #6053⋊C8 |
| Sylow | C52 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #6053⋊C2 |
| commutator | C5⋊D5 | C4×C8 |
| Fitting | C4×C52 | M16 |
| socle | C2×C52 | #97 |
| prime radical | C2×C5⋊D5 | C42 |
| cosocle | C4×#1043 | C22 |
| hypocenter | C52 | #322 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C4 | |
103 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,c^2=e,d^2=f,b^a=be,g^a=g^4,g^b=h,h^b=g^2,g^c=g^2,h^c=h^2,g^e=g^4,h^e=h^452 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5643);