Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2245 |
132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 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=eg,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,c^b=cg,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #2245×D83, C2×#24909707, #35559724, … |
| maximal normal subgroup of | #2245×D83, C2×#24909707, #35559724, … |
| maximal quotient of | #35320788, #35322338, #35322339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6754);