Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C5×#168 |
| derived | C5 ⋊ C2×C4×C5×C8 |
| Sylow | C52 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42×C5 | D5 |
| commutator, hypocenter | C5 | C2×C4×C5×C8 |
| Frattini | C2×C4 | C22×C5×D5 |
| Fitting | C2×C42×C52 | C2 |
| socle, prime radical | C23×C52 | C2×C4 |
| cosocle | C2×C4×C5 | C23×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C42×C5 | |
432 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4533);