Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
| direct product | D16×C5⋊D5 |
| Fitting | C52×D16 ⋊ C2 |
| Sylow | C52 ⋊ C2×D16 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D16×C5⋊D5, C5⋊D5×#509, D16×#1043, … |
| maximal normal subgroup of | C2×D16×C5⋊D5, C5⋊D5×#509, D16×#1043, … |
| maximal quotient of | C2×D16×C5⋊D5, C5⋊D5×#357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5125);