Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C83⋊C16) |
| Sylow | C83 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^82,c^b=ce1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C16×D83, C2×Q8⋊(C83⋊C16), #35314205, … |
| maximal normal subgroup of | Q8⋊C16×D83, C2×Q8⋊(C83⋊C16), #35314205, … |
| maximal quotient of | #35291186, #35291216, #35291308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2489);