Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2935 |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,f^2=g,b^a=be,h^a=h^82,d^b=dg,h^b=h^82,d^c=dg1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298877, #35298881, #35298891, … |
| maximal normal subgroup of | #35298877, #35298881, #35298891, … |
| maximal quotient of | #35376164, #35376174, #35376183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13256);