Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×C4×C22⋊(C5⋊D5) |
| Fitting | C23×C4×C52 ⋊ C2 |
| Sylow | C52 ⋊ C2×C4×D4 |
1704 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1704 conjugacy classes of subgroups — too many to draw. Only its 459 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 | C2×C4×D4×C5⋊D5 |
| maximal normal subgroup of | C2×C4×D4×C5⋊D5 |
| maximal quotient of | C2×#13102877, C2×#13103008 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9668);