Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #64686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#64686 |
| Sylow | C52 ⋊ #347 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72220685, C5×#10601711, #72220753, … |
| maximal normal subgroup of | #72220685, C5×#10601711, #72220753, … |
| maximal quotient of | C5×#10597933 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1728);