Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87837 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#87838 |
| Sylow | C52 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D52⋊C2 |
| commutator, cosocle | #1039 | C23 |
| Frattini | C2 | C2×D52⋊C2 |
| Fitting, socle | C22×C52 | D4 |
| prime radical | C2×#6037 | C2 |
| hypocenter | C52 | C2×SD16 |
| LCS | G ▷ #1039 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 | |
125 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | #13103391, #13104277, C4×#87838, … |
| maximal normal subgroup of | #13103391, #13104277, C4×#87838, … |
| maximal quotient of | #13104185, #13104186, #13104206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1055);