Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×#4078 |
| Fitting | C22×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ C2×AGL(1,ℤ/8) |
832 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13106298, C2×C5×#65366, C2×#13101713, … |
| maximal normal subgroup of | C2×#13106298, C2×C5×#65366, C2×#13101713, … |
| maximal quotient of | C5×#10615769, C5×#10614894, C5×D3×#4078 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9305);