Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5 |
| direct product | C4×#87902 |
| Fitting | C4×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ C4×#41 |
1240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#41×C5⋊D5, #72221182, #72242689 |
| maximal normal subgroup of | C4×#41×C5⋊D5, #72221182, #72242689 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9428);