Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2070 |
196 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 65 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=de,b^2=d,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,f^b=fg,h^b=h^82,d^c=dg925 conjugacy classes — view the full character table.
| maximal subgroup of | #2070×D83, C2×#24908864, #35433129, … |
| maximal normal subgroup of | #2070×D83, C2×#24908864, #35433129, … |
| maximal quotient of | #35309036, #35309038, #35309040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5911);