Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | Q16×C5⋊D5 |
| Fitting | C52×Q16 ⋊ C2 |
| Sylow | C52 ⋊ C2×Q16 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #13100286, #13100288, #13100378, … |
| maximal normal subgroup of | #13100286, #13100288, #13100378, … |
| maximal quotient of | #13102653, #13102655, #13102657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 896);