Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2162 |
160 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291245, #35291246, #35291250, … |
| maximal normal subgroup of | #35291245, #35291246, #35291250, … |
| maximal quotient of | #35319403, C4×C22⋊(C83⋊C16), C4×C4⋊(C83⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6309);