Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#6029⋊C5 |
| unambiguous semidirect product | (C2×#6029)⋊C5 |
| derived | C52 ⋊ C2×C5×C8 |
| Sylow | H(3,𝔽5) ⋊ C2×C8 |
109 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 146);