Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×#170 |
| derived | C5 ⋊ C22×C5×C8 |
| Sylow | C52 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C22×C5×C8 |
| Frattini | C2 | C22×C5×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C23×C52 | C4 |
| cosocle | Dic5 | C23×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C5 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13099832, C5×#64918, C2×Dic5×#170, … |
| maximal normal subgroup of | #13099832, C5×#64918, C2×Dic5×#170, … |
| maximal quotient of | C22×C5×#674, C2×C5×#3998, C2×C4×C5×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1076);