Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #3381 |
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=de,h^b=h^82,f^c=fg814 conjugacy classes — view the full character table.
| maximal subgroup of | #35394273, #35394280, #35394378, … |
| maximal normal subgroup of | #35394273, #35394280, #35394378, … |
| maximal quotient of | #35421004, #35421017, #35422809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17389);