Finite Group DatabasebetaFinite Group Databasebeta| order | 1808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#90673 |
| unambiguous semidirect product | (C2×#90673)⋊C2 |
| Fitting | C22×C113 ⋊ C4 |
| Sylow | C113 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 452 |
Polycyclic presentation:
2^4,113|a^2=d,b^a=bc,e^a=e^98,e^d=e^112122 conjugacy classes — view the full character table.
| maximal subgroup of | #16813680, #16813681, C2×C22⋊#90673, … |
| maximal normal subgroup of | #16813680, #16813681, C2×C22⋊#90673, … |
| maximal quotient of | (C2×#90673)⋊C4, C22⋊#11744753, #16813679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1808, 45);