Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4×C5 |
| direct product | M16×#1039 |
| Sylow | C52 ⋊ C4×M16 |
568 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 271 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 | C4×M16×C5⋊D5, #72220962, #72221170, … |
| maximal normal subgroup of | C4×M16×C5⋊D5, #72220962, #72221170, … |
| maximal quotient of | #72221022 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5332);