Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D313⋊M16 |
| Sylow | C313 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,d^2=e,b^a=be,f^a=f^25,f^c=f^312,f^d=f^312644 conjugacy classes — view the full character table.
| maximal subgroup of | #34095019, #34095021, #34095023, … |
| maximal normal subgroup of | #34095019, #34095021, #34095023, … |
| maximal quotient of | #34095111, C4×#19097570, C4×#19097571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 231);