Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2155 |
144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 81 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=d,c^2=g,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^82,e^b=eg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319784, #35319785, #35319832, … |
| maximal normal subgroup of | #35319784, #35319785, #35319832, … |
| maximal quotient of | #35315958, #35315961, #35316035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6284);