Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#1043 |
| Fitting | C23×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×C22⋊C4 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | #13099934, #13099935, #13099936, … |
| maximal normal subgroup of | #13099934, #13099935, #13099936, … |
| maximal quotient of | C2×#11716867, #13104757, C2×#11716871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1104);