Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #417×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3036 |
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^82,f^c=fg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35438974, #35438978, #35438985, … |
| maximal normal subgroup of | #35438974, #35438978, #35438985, … |
| maximal quotient of | #35388181, #35388187, #35388192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13973);