Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D25⋊C8 |
| unambiguous semidirect product | D25⋊(C2×C8) |
| derived, Sylow | C25 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1035 |
| commutator, hypocenter | C25 | C22×C8 |
| Frattini | C2×C5 | C22×AGL(1,𝔽5) |
| Fitting | C2×C4×C25 | C4 |
| socle | C22×C5 | C2×AGL(1,𝔽5) |
| prime radical | C22×D25 | C4 |
| cosocle | Dic25 | C23 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C4 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13097861, (C2×#1035)⋊C8, #13097885, … |
| maximal normal subgroup of | #13097861, (C2×#1035)⋊C8, #13097885, … |
| maximal quotient of | C4×D25⋊C8, D25⋊(C4⋊C8), #13098670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 203);