Finite Group DatabasebetaFinite Group Databasebeta| order | 2096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D131)⋊C4 |
| Fitting | C2×C4×C131 ⋊ C2 |
| Sylow | C131 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1048 |
Polycyclic presentation:
2^4,131|a^2=d,b^a=bc,e^b=e^130530 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D131, C2×(C2×D131)⋊C4, #16862203, … |
| maximal normal subgroup of | C22⋊C4×D131, C2×(C2×D131)⋊C4, #16862203, … |
| maximal quotient of | C131⋊#95, (C2×D131)⋊C8, #16862160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2096, 17);