Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D5×D5⋊M16 |
| unambiguous semidirect product | D5⋊(D5×M16) |
| Sylow | C52 ⋊ C22×M16 |
623 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72221499, #72221502, #72221503, … |
| maximal normal subgroup of | #72221499, #72221502, #72221503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9953);