Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×#10597845)⋊C4 |
| unambiguous semidirect product | D157⋊#95 |
| Fitting | C22×C4×C157 ⋊ C4 |
| Sylow | C157 ⋊ C2×#95 |
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
664 conjugacy classes — view the full character table.
| maximal subgroup of | #34114973, #34115009, #34115011, … |
| maximal normal subgroup of | #34114973, #34115009, #34115011, … |
| maximal quotient of | C4×(C2×#10597845)⋊C4, #34115309, #34115310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1484);