Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C4⋊C4×C5⋊D5 |
| Fitting | C52×C4⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C2×C4⋊C4 |
368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13100253, #13100345, #13100644, … |
| maximal normal subgroup of | #13100253, #13100345, #13100644, … |
| maximal quotient of | #13102510, #13102513, #13102514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 870);