Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26×C5 |
| direct product | C23×C5×C5⋊D5 |
| Fitting, socle | C23×C53 ⋊ C2 |
| derived | C52 ⋊ C24×C5 |
| Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C53 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C5 | |
1456 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, 961);