Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D52⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D52⋊C2 |
| unambiguous semidirect product | D52⋊C23 |
| Fitting, socle | C22×C52 ⋊ D4 |
| Sylow | C52 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D52⋊C2 |
| commutator, cosocle | C5⋊D5 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52 | D4 |
| hypocenter | C52 | C22×D4 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C22 | |
397 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #13103360, #13103371, #13103373, … |
| maximal normal subgroup of | #13103360, #13103371, #13103373, … |
| maximal quotient of | C2×#11717378, C2×#11717379, #13107656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1201);