Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×D52⋊C2 |
| Fitting | C52×C8 ⋊ D4 |
| Sylow | C52 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D52⋊C2 |
| commutator | C5⋊D5 | C22×C8 |
| Frattini | C4 | C2×D52⋊C2 |
| Fitting | C52×C8 | D4 |
| socle | C2×C52 | C4×D4 |
| prime radical | C2×D52⋊C2 | C4 |
| cosocle | C4×C5⋊D5 | C23 |
| hypocenter | C52 | C8×D4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C8 | |
232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6496);