Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | D5×#674 |
| derived, Sylow | C52 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C2×C16 |
| Fitting | C4×C52 | C2×C4 |
| socle | C2×C52 | C2×C8 |
| prime radical | C2×C5×D5 | C8 |
| cosocle | C5×#168 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#674, #13103265, #13103268, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#674, #13103265, #13103268, … |
| maximal quotient of | D5×#3928, #13099744, Dic5×#674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 405);