Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1280 |
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 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=d,b^2=e,d^2=g,b^a=bc,c^a=cf,h^a=h^82,d^b=df1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291149, #35291150, #35291151, … |
| maximal normal subgroup of | #35291149, #35291150, #35291151, … |
| maximal quotient of | #35290934, #35290936, #35290942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2353);