Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14578818 |
| Fitting | C4×C313 ⋊ C8 |
| Sylow | C313 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^5,f^d=f^25,f^e=f^312176 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14578818, Q8⋊#14578818, #34095241, … |
| maximal normal subgroup of | D4⋊#14578818, Q8⋊#14578818, #34095241, … |
| maximal quotient of | #34095241, #34095242, (C2×#14578818)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 239);