Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2215 |
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 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,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^822662 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291958, #35291960, #35291964, … |
| maximal normal subgroup of | #35291958, #35291960, #35291964, … |
| maximal quotient of | #35318610, #35318661, #35318729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6596);