Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#11716670 |
| Sylow | C52 ⋊ C2×#97 |
584 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#97×C5⋊D5, C2×#13102877, C2×#13100238, … |
| maximal normal subgroup of | C2×#97×C5⋊D5, C2×#13102877, C2×#13100238, … |
| maximal quotient of | C2×#13099498 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5136);