Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #87863 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5 |
| direct product | C22×#87867 |
| Sylow | C52 ⋊ C22×M16 |
832 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11717448 |
| maximal normal subgroup of | C22×#11717448 |
| maximal quotient of | C22×#11716895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10129);