Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1989 |
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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=def,c^2=eg,d^2=g,f^2=g,b^a=bd,c^a=ce,d^b=dg,f^b=fg,h^b=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296879, #35296881, #35296886, … |
| maximal normal subgroup of | #35296879, #35296881, #35296886, … |
| maximal quotient of | #35304392, #35304397, #35304536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5465);