Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C52×C8 ⋊ C22 |
| Sylow | C52 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D52 |
| commutator, socle | C2×C52 | C23×C4 |
| Fitting | C2×C52×C8 | C22 |
| prime radical | D5×#709 | C2 |
| cosocle | C4×C52 | C24 |
| hypercenter | C2×C8 | D52 |
| hypocenter | C52 | #568 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C2×C8 | |
578 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|d^2=e,e^2=f,d^a=df,g^a=g^4,c^b=cf,h^b=h^4178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8111);