Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #464×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3035 |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^82,f^c=fg,h^c=h^82,h^d=h^82817 conjugacy classes — view the full character table.
| maximal subgroup of | #3035×D83, C2×#24916917, #36271276, … |
| maximal normal subgroup of | #3035×D83, C2×#24916917, #36271276, … |
| maximal quotient of | #35386825, #35386833, #35386840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13964);