Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | #106×C5⋊D5 |
| Fitting | C52×#106 ⋊ C2 |
| Sylow | C52 ⋊ C2×#106 |
520 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | #106×#1043, C5⋊D5×#442, #72220668, … |
| maximal normal subgroup of | #106×#1043, C5⋊D5×#442, #72220668, … |
| maximal quotient of | C5⋊D5×#334, C5⋊D5×#365, C2×#106×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5074);