Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#66125 |
| Fitting | C23×C4×C52 ⋊ C2 |
| Sylow | C52 ⋊ #525 |
896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72221094, C5×#10615769, #72223286, … |
| maximal normal subgroup of | #72221094, C5×#10615769, #72223286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9297);