Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D52 |
| Fitting | C2×C4×C52 ⋊ C22 |
| derived, Sylow | C52 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D52 |
| commutator, hypocenter | C52 | C23×C4 |
| Frattini | C2 | C22×D52 |
| Fitting | C2×C4×C52 | C22 |
| socle | C22×C52 | C23 |
| prime radical | C22×D52 | C2 |
| cosocle | C2×C52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
526 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3952, #13101109, #13101110, … |
| maximal normal subgroup of | D5×#3952, #13101109, #13101110, … |
| maximal quotient of | C4×D5×Dic10, #13104954, C4×#87870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1126);