Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1407 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=g,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^82,d^c=dfg,e^d=eg547 conjugacy classes — view the full character table.
| maximal subgroup of | #1407×D83, C2×#24905622, #35324689, … |
| maximal normal subgroup of | #1407×D83, C2×#24905622, #35324689, … |
| maximal quotient of | #35291784, #35291822, #35291913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2669);