Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C16 · Schur multiplier (H2) = C5 |
| direct product | C5×#87756 |
| derived | C52 ⋊ C5×C16 |
| Sylow | C53 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C8 | C5⋊D5 |
| commutator, hypocenter | C52 | C5×C16 |
| Frattini | C8 | C5×C5⋊D5 |
| Fitting | C53×C8 | C2 |
| socle, prime radical | C2×C53 | C8 |
| cosocle | C52×C8 | C2×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C5×C8 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 469);