Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of AGL(1,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×#170 |
| derived, Sylow | C52 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)2 |
| commutator, hypocenter | C52 | C4×C8 |
| Fitting, socle | C2×C52 | C42 |
| prime radical | C2×C5×D5 | C2×C4 |
| cosocle | D5×Dic5 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×D5⋊C8, AGL(1,𝔽5)×#700, #13107447, … |
| maximal normal subgroup of | AGL(1,𝔽5)×D5⋊C8, AGL(1,𝔽5)×#700, #13107447, … |
| maximal quotient of | AGL(1,𝔽5)×#674, #13103265, #13103268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 958);