Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1980 |
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=df,c^2=e,d^2=g,b^a=bd,c^a=ce,h^a=h^82,d^b=dg,f^b=fg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296283, #35296288, #35296304, … |
| maximal normal subgroup of | #35296283, #35296288, #35296304, … |
| maximal quotient of | #35303356, #35303360, #35303365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5429);