Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#6016 |
| derived, Sylow | C25 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #1035 |
| commutator, hypocenter | C25 | C22×C8 |
| Frattini | C2×C5 | C22×AGL(1,𝔽5) |
| Fitting | C23×C25 | C4 |
| socle, prime radical | C23×C5 | AGL(1,𝔽5) |
| cosocle | Dic25 | C23 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C23 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13097903, #13098680, #13098681, … |
| maximal normal subgroup of | #13097903, #13098680, #13098681, … |
| maximal quotient of | C22×#87709, C2×#11716414, C2×C4×#6016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 213);