Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C4×C22⋊(C5⋊D5) |
| Fitting | C22×C4×C52 ⋊ C2 |
| Sylow | C52 ⋊ C4×D4 |
376 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #13101489, #13101490, #13101498, … |
| maximal normal subgroup of | #13101489, #13101490, #13101498, … |
| maximal quotient of | C4×#87806, #13102794, C4×#87808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 907);