Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D5×#4054 |
| Fitting | C52×M16 ⋊ C22 |
| Sylow | C52 ⋊ C2×AGL(1,ℤ/8) |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | D52×AGL(1,ℤ/8), #72221384, #72221389 |
| maximal normal subgroup of | D52×AGL(1,ℤ/8), #72221384, #72221389 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8152);