Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #493×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2250 |
198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 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=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^b=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #35317882, #35317883, #35317889, … |
| maximal normal subgroup of | #35317882, #35317883, #35317889, … |
| maximal quotient of | #35319072, #35319082, #35319105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6774);