Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #481×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3091 |
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^c=h^82,h^d=h^82817 conjugacy classes — view the full character table.
| maximal subgroup of | #35376562, #35376564, #35376664, … |
| maximal normal subgroup of | #35376562, #35376564, #35376664, … |
| maximal quotient of | #35404194, #35405130, #35405622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14420);