Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ SD64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11716587 |
| commutator, Fitting, cosocle | C52×C16 | C22 |
| Frattini, hypercenter | C16 | D52 |
| socle | C2×C52 | D16 |
| prime radical | C5×D80 | C2 |
| hypocenter | C52 | SD64 |
| LCS | G ▷ C52×C16 ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|b^2=cdf,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,h^a=h^4,g^b=g^4169 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1595);