Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×D5×#168 |
| derived, Sylow | C52 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D52 |
| commutator, hypocenter | C52 | C23×C8 |
| Frattini | C4 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C23×C52 | C2×C4 |
| prime radical | C23×C5×D5 | C4 |
| cosocle | C4×C52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C4 | |
752 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 352 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8253);