Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #519×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3428 |
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^b=h^82,h^c=h^82,h^e=h^821462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35404275, #35405218, #35405237, … |
| maximal normal subgroup of | #35404275, #35405218, #35405237, … |
| maximal quotient of | #35562617, #35562632, #35562636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17712);