Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #421×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2901 |
738 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^82,d^c=dg,h^d=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35420357, #35420359, #35420361, … |
| maximal normal subgroup of | #35420357, #35420359, #35420361, … |
| maximal quotient of | #35370784, #35370785, #35370791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13056);