Finite Group DatabasebetaFinite Group Databasebeta| order | 37456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#22627296 |
| unambiguous semidirect product | (C2×#22627296)⋊C2 |
| Fitting | C22×C2341 ⋊ C4 |
| Sylow | C2341 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9364 |
Polycyclic presentation:
2^4,2341|a^2=d,b^a=bc,e^a=e^153,e^d=e^23402350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37456, 45);