Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87809 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | C2×#87811 |
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C2×SD16 |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #13101732, #13101733, #13101736, … |
| maximal normal subgroup of | #13101732, #13101733, #13101736, … |
| maximal quotient of | C2×#11716675, C2×#11716676, #13102850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 920);