Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×D20 |
| unambiguous semidirect product | C4⋊(D5×C25) |
| Fitting | C4×C5×C25 ⋊ C2 |
| Sylow | C5×C25 ⋊ D4 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14522120, #14522121, #14522122, … |
| maximal normal subgroup of | #14522120, #14522121, #14522122, … |
| maximal quotient of | C25×#677, C25×D40, C25×Dic20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 52);