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 ⋊ Q8×#41 |
1068 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296444, #35296448, #35371280, … |
| maximal normal subgroup of | #35296444, #35296448, #35371280, … |
| maximal quotient of | #35563715, #35563718, #35563826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18088);