Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C5 |
| direct product | #108×C5⋊D5 |
| Fitting | C52×#108 ⋊ C2 |
| Sylow | C52 ⋊ C2×#108 |
424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#365, #108×#1043, #72242230, … |
| maximal normal subgroup of | C5⋊D5×#365, #108×#1043, #72242230, … |
| maximal quotient of | C5⋊D5×#334, C2×#108×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5107);