Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4×C5 |
| direct product | C4×#87804 |
| Sylow | C52 ⋊ C4×M16 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×M16×C5⋊D5, #72220958, #72220984, … |
| maximal normal subgroup of | C4×M16×C5⋊D5, #72220958, #72220984, … |
| maximal quotient of | #72221022 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5137);