Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#87767 |
| derived, Sylow | C52 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D52 |
| commutator, hypocenter | C52 | C22×C8 |
| Frattini | C4 | C2×D52 |
| Fitting | C2×C4×C52 | C22 |
| socle | C22×C52 | C2×C4 |
| prime radical | C22×C5⋊D5 | C4 |
| cosocle | C4×C52 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13099809, #13099894, #13099895, … |
| maximal normal subgroup of | #13099809, #13099894, #13099895, … |
| maximal quotient of | #13100432, #13100434, #13100477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 593);