Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C23×#4147 |
| Fitting | C24×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C23×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D5 |
| commutator, cosocle | C2×C5 | C27 |
| Frattini | C2 | C26×D5 |
| Fitting | C24×C5×Q8 | C2 |
| socle | C24×C5 | C24 |
| hypercenter | C24×Q8 | D5 |
| hypocenter | C5 | C23×2−1+4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C24×Q8 | |
59806 conjugacy classes of subgroups; only the 32139 normal subgroups are shown.
This group has 59806 conjugacy classes of subgroups — too many to draw. Only its 32139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
296 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1083458);