Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#65529 |
| Sylow | C52 ⋊ #410 |
480 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72221125, C5×#10602647, #72223332, … |
| maximal normal subgroup of | #72221125, C5×#10602647, #72223332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4846);