Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×#11717270 |
| Fitting | C2×C52×#41 ⋊ C2 |
| Sylow | C52 ⋊ C2×#135 |
1064 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#135×C5⋊D5, C2×#13102686, C2×#13103008 |
| maximal normal subgroup of | C2×#135×C5⋊D5, C2×#13102686, C2×#13103008 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9704);