Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#65421 |
| Fitting | C2×C52×M16 ⋊ C2 |
| Sylow | C52 ⋊ #413 |
368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72221305, C5×#10610434, #72223484, … |
| maximal normal subgroup of | #72221305, C5×#10610434, #72223484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4744);