Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C5 |
| direct product | C2×#11716688 |
| Fitting | C22×C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ C2×#102 |
808 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 259 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
412 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#102×C5⋊D5, C2×#13102647, C2×#13102575 |
| maximal normal subgroup of | C2×#102×C5⋊D5, C2×#13102647, C2×#13102575 |
| maximal quotient of | C2×#13099552 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5326);