Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#10597845 |
| unambiguous semidirect product | D157⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#10597845)⋊C23 |
| Fitting | C24×C157 ⋊ C4 |
| Sylow | C157 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups.
664 conjugacy classes — view the full character table.
| maximal subgroup of | #34115309, #34115310, #34115317, … |
| maximal normal subgroup of | #34115309, #34115310, #34115317, … |
| maximal quotient of | C22×(C2×#10597845)⋊C4, C2×C4×C22⋊#10597845, C2×#23758214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1610);