Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #462×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3120 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^82,f^c=fg,h^c=h^82,h^d=h^82811 conjugacy classes — view the full character table.
| maximal subgroup of | #3120×D83, C2×#24917676, #36272772, … |
| maximal normal subgroup of | #3120×D83, C2×#24917676, #36272772, … |
| maximal quotient of | #35404513, #35407479, #35407507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14723);