Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#99×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2044 |
382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^82,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #2044×D83, C2×#24908713, #35432166, … |
| maximal normal subgroup of | #2044×D83, C2×#24908713, #35432166, … |
| maximal quotient of | #35307671, #35307673, #35307678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5760);