Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #459×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3325 |
460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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=eg,b^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^82,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^c=h^82,h^d=h^82808 conjugacy classes — view the full character table.
| maximal subgroup of | #35393984, #35393986, #35394044, … |
| maximal normal subgroup of | #35393984, #35393986, #35394044, … |
| maximal quotient of | #35420022, #35420861, #35421718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16755);