Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #533×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^82,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35370986, #35370992, #35371087, … |
| maximal normal subgroup of | #35370986, #35370992, #35371087, … |
| maximal quotient of | #35563093, #35563105, #35563109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17941);