Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2110 |
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 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=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,c^b=cg,d^b=dg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319236, #35319238, #35319425, … |
| maximal normal subgroup of | #35319236, #35319238, #35319425, … |
| maximal quotient of | #35313408, #35313410, #35313412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6114);