Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #2165 |
128 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 55 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=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,e^b=eg,e^c=eg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35313833, #35313835, #35313837, … |
| maximal normal subgroup of | #35313833, #35313835, #35313837, … |
| maximal quotient of | #35319419, #35319472, #35319737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6319);