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 | C4×D5×AGL(1,𝔽5) |
| Fitting | C4×C52 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C2 | C2×D5×AGL(1,𝔽5) |
| Fitting | C4×C52 | C2×C4 |
| socle | C2×C52 | C22×C4 |
| prime radical | C2×D52 | C22 |
| cosocle | C2×C5×D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
224 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13103258, #13103259, C8×D5×AGL(1,𝔽5), … |
| maximal normal subgroup of | #13103258, #13103259, C8×D5×AGL(1,𝔽5), … |
| maximal quotient of | C8×D5×AGL(1,𝔽5), AGL(1,𝔽5)×#676, D5×#3992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 993);