Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic10 |
| unambiguous semidirect product | C5⋊(Q8×C25) |
| Sylow | C5×C25 ⋊ Q8 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14522124, #14522125, #14522126, … |
| maximal normal subgroup of | #14522124, #14522125, #14522126, … |
| maximal quotient of | C25×#683, C25×C4⋊Dic5, C2×C25×Dic10 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 48);