Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | Dic5×#170 |
| derived, Sylow | C52 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C4×C8 |
| Fitting, socle, prime radical | C22×C52 | C2×C4 |
| cosocle | C2×C5×Dic5 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #1702, #170⋊#170, #13103281, … |
| maximal normal subgroup of | #1702, #170⋊#170, #13103281, … |
| maximal quotient of | #168×#170, #13099747, Dic5×#674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 410);