Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#87835 |
| Sylow | C52 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D52⋊C2 |
| commutator | C5⋊D5 | C23×C4 |
| Frattini | C2 | C22×D52⋊C2 |
| Fitting, socle | C23×C52 | D4 |
| prime radical | C23×D52 | C2 |
| cosocle | C2×C5⋊D5 | C24 |
| hypocenter | C52 | C22×C22⋊C4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C23 | |
1284 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 185 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, 10040);