Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#14270406 |
| unambiguous semidirect product | D461⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#14270406)⋊C22 |
| Fitting | C23×C461 ⋊ C4 |
| Sylow | C461 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3688 |
940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44442953, #44442954, C4×C22⋊#14270406, … |
| maximal normal subgroup of | #44442953, #44442954, C4×C22⋊#14270406, … |
| maximal quotient of | C2×(C2×#14270406)⋊C4, C4×C22⋊#14270406, #44443017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 223);