Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #344×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2009 |
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^82,c^b=cf,d^b=dg,h^b=h^82,d^c=dg,e^c=eg,h^c=h^82925 conjugacy classes — view the full character table.
| maximal subgroup of | #2009×D83, C2×#24908526, #35431409, … |
| maximal normal subgroup of | #2009×D83, C2×#24908526, #35431409, … |
| maximal quotient of | #35304722, #35304736, #35304750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5573);