Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2162 |
160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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,h^b=h^82,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35314233, #35314235, #35314238, … |
| maximal normal subgroup of | #35314233, #35314235, #35314238, … |
| maximal quotient of | #35319401, #35319430, C4⋊C16×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6308);