Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#1035 |
| Fitting | C8×C25 ⋊ C4 |
| derived, Sylow | C25 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1035 |
| commutator, hypocenter | C25 | C4×C8 |
| Frattini | C4×C5 | C2×AGL(1,𝔽5) |
| Fitting | C8×C25 | C4 |
| socle | C2×C5 | C4×AGL(1,𝔽5) |
| prime radical | C2×D25 | C2×C4 |
| cosocle | C4×D25 | C22 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C8 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#1035, #13097830, C2×C8×#1035, … |
| maximal normal subgroup of | C16×#1035, #13097830, C2×C8×#1035, … |
| maximal quotient of | C16×#1035, #13097830, C8×#6016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 68);