Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×#170 |
| derived, Sylow | C52 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C22×C8 |
| Frattini | C2 | C2×D5×AGL(1,𝔽5) |
| Fitting, socle | C22×C52 | C2×C4 |
| prime radical | C22×C5×D5 | C4 |
| cosocle | C5×Dic5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×AGL(1,𝔽5))⋊#170, C4×D5×#170, #13103640, … |
| maximal normal subgroup of | (C2×AGL(1,𝔽5))⋊#170, C4×D5×#170, #13103640, … |
| maximal quotient of | #170×Dic10, #13103477, #13103478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1001);