Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5 |
| direct product | C4×#87900 |
| Fitting | C2×C42×C52 ⋊ C2 |
| Sylow | C52 ⋊ C4×#41 |
1240 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 363 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 | C4×#41×C5⋊D5, #72221185, #72221191, … |
| maximal normal subgroup of | C4×#41×C5⋊D5, #72221185, #72221191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9354);