Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2961 |
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,c^b=cg,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298540, #35298544, #35298554, … |
| maximal normal subgroup of | #35298540, #35298544, #35298554, … |
| maximal quotient of | #35402360, #35402380, #35403040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13447);