Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D317⋊M16 |
| Sylow | C317 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,d^2=e,b^a=be,f^a=f^203,f^c=f^316,f^d=f^316652 conjugacy classes — view the full character table.
| maximal subgroup of | #35204090, #35204092, #35204094, … |
| maximal normal subgroup of | #35204090, #35204092, #35204094, … |
| maximal quotient of | #35204182, C4×#19099583, C4×#19099584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 231);