Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C83⋊#1304 |
| Sylow | C83 ⋊ #1304 |
396 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 65 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=d,b^2=e,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291887, #35291888, #35291983, … |
| maximal normal subgroup of | #35291887, #35291888, #35291983, … |
| maximal quotient of | #35290974, #35290975, #35290981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2414);