Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#10597845 |
| unambiguous semidirect product | D157⋊(C2×C4⋊C4) |
| Fitting | C22×C4×C157 ⋊ C4 |
| Sylow | C157 ⋊ C22×C4⋊C4 |
418 conjugacy classes of subgroups.
664 conjugacy classes — view the full character table.
| maximal subgroup of | #34115313, #34115314, #34115316, … |
| maximal normal subgroup of | #34115313, #34115314, #34115316, … |
| maximal quotient of | C22×(C2×#10597845)⋊C4, C2×C4×C4⋊#10597845, C2×#23758215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1611);