Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #3042 |
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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|a^2=g,b^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=dg,h^b=h^82,f^c=fg934 conjugacy classes — view the full character table.
| maximal subgroup of | #35441799, #35441800, #35452288, … |
| maximal normal subgroup of | #35441799, #35441800, #35452288, … |
| maximal quotient of | #35389624, #35389633, #35389642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14024);