Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1371 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^822668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291854, #35291855, #35291857, … |
| maximal normal subgroup of | #35291854, #35291855, #35291857, … |
| maximal quotient of | #35291144, #35291274, #35292081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2582);