Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D83)⋊C32 |
| Fitting | C2×C32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C32×D83, C2×(C2×D83)⋊C32, #35324596, … |
| maximal normal subgroup of | C22⋊C32×D83, C2×(C2×D83)⋊C32, #35324596, … |
| maximal quotient of | #35291742, #35291802, #35291841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2647);