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.
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,h^a=h^82,c^b=cf,f^b=fg,h^b=h^82,d^c=dg,h^c=h^82925 conjugacy classes — view the full character table.
| maximal subgroup of | #2070×D83, C2×#24908865, #35433127, … |
| maximal normal subgroup of | #2070×D83, C2×#24908865, #35433127, … |
| maximal quotient of | #35309041, #35309055, #35309069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5912);