Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1400 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^82,d^b=dg1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291746, #35291747, #35291748, … |
| maximal normal subgroup of | #35291746, #35291747, #35291748, … |
| maximal quotient of | #35291743, #35291803, #35291845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2650);