Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×C5×#681 |
| Sylow | C52 ⋊ C4×M16 |
392 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#11716936, C5×#10610711, #72223434, … |
| maximal normal subgroup of | C4×#11716936, C5×#10610711, #72223434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4535);