Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #529×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3461 |
1012 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^b=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296199, #35296201, #35376750, … |
| maximal normal subgroup of | #35296199, #35296201, #35376750, … |
| maximal quotient of | #35563097, #35563101, #35563363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17939);