Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#66169 |
| Fitting | C52×H(5,𝔽2) ⋊ C2 |
| Sylow | C52 ⋊ #576 |
702 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72221224, C5×#10619178, #72223278, … |
| maximal normal subgroup of | #72221224, C5×#10619178, #72223278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9341);