Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2×C5 |
| direct product | C16×C5⋊D5 |
| Fitting | C52×C16 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C16 |
| Frattini | C8 | C2×C5⋊D5 |
| Fitting | C52×C16 | C2 |
| socle | C2×C52 | C2×C8 |
| prime radical | C2×C5⋊D5 | C8 |
| cosocle | C52×C8 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C16 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #13099237, #13099239, C32×C5⋊D5, … |
| maximal normal subgroup of | #13099237, #13099239, C32×C5⋊D5, … |
| maximal quotient of | C32×C5⋊D5, #13099481, C16×#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 323);