Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #87863 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C5 |
| direct product | C22×C22⋊#1044 |
| Fitting | C24×C52 ⋊ C4 |
| Sylow | C52 ⋊ C22×C22⋊C4 |
2096 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 2096 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13107767, C22×#11717375, C2×#13107590, … |
| maximal normal subgroup of | C2×#13107767, C22×#11717375, C2×#13107590, … |
| maximal quotient of | #72221035, C2×#13104909, #72221080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10130);