Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2061 |
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 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|a^2=d,b^2=d,c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^82,c^b=cf,e^b=eg,e^c=eg,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #35317322, #35317324, #35317336, … |
| maximal normal subgroup of | #35317322, #35317324, #35317336, … |
| maximal quotient of | #35308813, #35308818, #35308828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5861);