Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #475×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3304 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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=e,b^2=g,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^82,f^c=fg,h^d=h^82814 conjugacy classes — view the full character table.
| maximal subgroup of | #35394199, #35394207, #35394214, … |
| maximal normal subgroup of | #35394199, #35394207, #35394214, … |
| maximal quotient of | #35419870, #35420684, #35421620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16446);