Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #64845 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#64863 |
| Fitting | C42×C52 ⋊ C4 |
| Sylow | C52 ⋊ H(3,ℤ/4) |
203 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | #72221505, C5×#10604619, #72221596, … |
| maximal normal subgroup of | #72221505, C5×#10604619, #72221596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2405);