Finite Group DatabasebetaFinite Group Databasebeta| order | 16496 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D1031)⋊C4 |
| Fitting | C2×C4×C1031 ⋊ C2 |
| Sylow | C1031 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8248 |
Polycyclic presentation:
2^4,1031|a^2=d,b^a=bc,e^b=e^10304130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1031, C2×(C2×D1031)⋊C4, #45682381, … |
| maximal normal subgroup of | C22⋊C4×D1031, C2×(C2×D1031)⋊C4, #45682381, … |
| maximal quotient of | C1031⋊#95, (C2×D1031)⋊C8, #45682338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16496, 17);