Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C5 |
| direct product | C8×C22⋊(C5⋊D5) |
| Fitting | C22×C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ C8×D4 |
536 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D4×C5⋊D5 |
| maximal normal subgroup of | C8×D4×C5⋊D5 |
| maximal quotient of | #72253071 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5323);