Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#87830 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C2 | C2×D5⋊AGL(1,𝔽5) |
| Fitting, socle | C22×C52 | C2×C4 |
| prime radical | C22×C5⋊D5 | C22 |
| cosocle | C2×C5⋊D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22 | |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #13103283, #13103302, #13103352, … |
| maximal normal subgroup of | #13103283, #13103302, #13103352, … |
| maximal quotient of | #13103879, #13103890, #13103896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1025);