Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4×C5 |
| direct product | C2×C4×#6029 |
| derived, Sylow | C52 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C4×C8 |
| Frattini | C2×C4 | C22×C5⋊D5 |
| Fitting | C2×C42×C52 | C2 |
| socle, prime radical | C23×C52 | C2×C4 |
| cosocle | C2×C4×C52 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C42 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5135);