Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×#4058 |
| Fitting | C2×C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ C2×#135 |
608 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13105821, C5×#10612597, #72242557 |
| maximal normal subgroup of | C2×#13105821, C5×#10612597, #72242557 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9262);