Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C32 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#3926 |
| derived, Sylow | C5 ⋊ C2×C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C16 | D5 |
| commutator, hypocenter | C5 | C2×C4×C32 |
| Frattini | C2×C16 | C22×D5 |
| Fitting | C2×C4×C5×C16 | C2 |
| socle, prime radical | C23×C5 | C2×C16 |
| cosocle | C2×C5×C16 | C23 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C4×C16 | |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89738);