Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of (C2×AGL(1,𝔽5))⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#87828 |
| Sylow | C52 ⋊ C2×M16 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | #13103288, #13103640, #13103642, … |
| maximal normal subgroup of | #13103288, #13103640, #13103642, … |
| maximal quotient of | #13103513, #13103517, #13103520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1007);