Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #410×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3025 |
766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|d^2=g,b^a=be,c^a=cf,h^a=h^82,f^b=fg,e^c=eg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35321691, #35321693, #35321698, … |
| maximal normal subgroup of | #35321691, #35321693, #35321698, … |
| maximal quotient of | #35376675, #35376677, #35376684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13904);