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×#87812 |
| Sylow | C52 ⋊ C2×Q16 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #13101742, #13101743, #13101746, … |
| maximal normal subgroup of | #13101742, #13101743, #13101746, … |
| maximal quotient of | #13102825, C2×#11716674, C2×#11716677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 922);