Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2667 |
408 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=g,c^2=eg,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^821672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35307624, #35307625, #35307631, … |
| maximal normal subgroup of | #35307624, #35307625, #35307631, … |
| maximal quotient of | #35331022, #35331037, #35331122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 10704);