Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #490×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3136 |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^82,h^c=h^82,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #3136×D83, C2×#24917818, #36273658, … |
| maximal normal subgroup of | #3136×D83, C2×#24917818, #36273658, … |
| maximal quotient of | #35404609, #35407053, #35407069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14865);