Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#65363 |
| Fitting | C52×#127 ⋊ C2 |
| Sylow | C52 ⋊ #496 |
396 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #72221314, C5×#10612011, #72223383, … |
| maximal normal subgroup of | #72221314, C5×#10612011, #72223383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4686);