Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2041 |
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,f^b=fg,e^c=eg,f^c=fg,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293104, #35293105, #35293111, … |
| maximal normal subgroup of | #35293104, #35293105, #35293111, … |
| maximal quotient of | #35307725, #35307730, #35307759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5741);