Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87770 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#87775 |
| Sylow | C52 ⋊ C2×Q16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | #13099994, #13099998, #13100534, … |
| maximal normal subgroup of | #13099994, #13099998, #13100534, … |
| maximal quotient of | #13100463, #13100469, #13100492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 611);