Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×#10597845 |
| Fitting | C4⋊C4×C157 ⋊ C4 |
| Sylow | C157 ⋊ C4×C4⋊C4 |
194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
430 conjugacy classes — view the full character table.
| maximal subgroup of | #102×#10597845, #103×#10597845, #34115907, … |
| maximal normal subgroup of | #102×#10597845, #103×#10597845, #34115907, … |
| maximal quotient of | #95×#10597845, #34115311, #34115313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1489);