Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#87827 |
| derived, Sylow | C52 ⋊ C2×C4×C8 |
351 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11717300, #72242288, #72242309 |
| maximal normal subgroup of | C4×#11717300, #72242288, #72242309 |
| maximal quotient of | #72242231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5995);