Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×#11717201 |
| Fitting | C2×C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C2×C4×D4 |
1704 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1704 conjugacy classes of subgroups — too many to draw. Only its 403 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D4×C5⋊D5 |
| maximal normal subgroup of | C2×C4×D4×C5⋊D5 |
| maximal quotient of | C2×#13102647, C2×#13102686 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9366);