Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87863 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C5 |
| direct product | C2×C22⋊#1044 |
| Fitting | C23×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×C22⋊C4 |
398 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
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×#11716892, #13104883, C2×#11716896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1117);