Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#11716684 |
| Sylow | C52 ⋊ C2×#106 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
412 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#106×C5⋊D5, C2×#13102575, C2×#13103012, … |
| maximal normal subgroup of | C2×#106×C5⋊D5, C2×#13102575, C2×#13103012, … |
| maximal quotient of | C2×#13099547 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5318);