Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2005 |
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=g,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,c^b=cf,d^b=dg,h^b=h^82,d^c=dg928 conjugacy classes — view the full character table.
| maximal subgroup of | #2005×D83, C2×#24908497, #35431310, … |
| maximal normal subgroup of | #2005×D83, C2×#24908497, #35431310, … |
| maximal quotient of | #35304619, #35304633, #35304675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5544);