Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C313 ⋊ C4 |
| Sylow | C313 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^25,c^b=ce,f^b=f^312,f^d=f^312404 conjugacy classes — view the full character table.
| maximal subgroup of | D313⋊#104, C2×#23756562, #34095149, … |
| maximal normal subgroup of | D313⋊#104, C2×#23756562, #34095149, … |
| maximal quotient of | #34095000, Q8⋊#14578816, #34095004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 211);