Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2233 |
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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=dg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^c=ef,f^c=fg,h^c=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #35317622, #35317623, #35317633, … |
| maximal normal subgroup of | #35317622, #35317623, #35317633, … |
| maximal quotient of | #35320694, #35320907, #35321343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6693);