Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #390×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2006 |
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,h^b=h^82,e^c=eg,h^c=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291928, #35291930, #35316467, … |
| maximal normal subgroup of | #35291928, #35291930, #35316467, … |
| maximal quotient of | #35304711, #35304718, #35304725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5551);