Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1942 |
248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,c^2=eg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^822668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291191, #35291193, #35291194, … |
| maximal normal subgroup of | #35291191, #35291193, #35291194, … |
| maximal quotient of | #35302946, #35302966, #35303052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5243);