Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2402 |
400 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 161 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=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^82,c^b=cg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35307540, #35307541, #35307545, … |
| maximal normal subgroup of | #35307540, #35307541, #35307545, … |
| maximal quotient of | #35326135, #35326136, #35326149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7818);