Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3937 |
| Fitting | C42×C52 ⋊ C2 |
| Sylow | C52 ⋊ #104 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #13100568, #13100569, #13100570, … |
| maximal normal subgroup of | #13100568, #13100569, #13100570, … |
| maximal quotient of | C5×#64671, C5×#64672, C5×#64679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 290);