Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #361×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2223 |
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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=dfg,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^b=h^82,e^c=eg,h^c=h^82682 conjugacy classes — view the full character table.
| maximal subgroup of | #2223×D83, C2×#24909592, #35558977, … |
| maximal normal subgroup of | #2223×D83, C2×#24909592, #35558977, … |
| maximal quotient of | #35318619, #35318636, #35318670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6639);