Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C23×#1044 |
| Fitting, socle | C23×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #1044 |
| commutator, hypocenter | C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | C4 |
| prime radical | C23×C5⋊D5 | C2 |
| cosocle | C5⋊D5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11716776, #13104112, #13104118, … |
| maximal normal subgroup of | C2×#11716776, #13104112, #13104118, … |
| maximal quotient of | C22×#87862, C22×#87863, C2×#11717448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1206);