Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D41⋊M16 |
| Sylow | C41 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^5,41|a^2=d,d^2=e,b^a=be,f^a=f^32,f^c=f^40,f^d=f^40100 conjugacy classes — view the full character table.
| maximal subgroup of | #14581203, #14581205, #14581207, … |
| maximal normal subgroup of | #14581203, #14581205, #14581207, … |
| maximal quotient of | #14581295, C4×#10620301, C4×#10620297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 231);