Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1340 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=g,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^82,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^82,d^c=dg922 conjugacy classes — view the full character table.
| maximal subgroup of | #1340×D83, C2×#24905452, #35314551, … |
| maximal normal subgroup of | #1340×D83, C2×#24905452, #35314551, … |
| maximal quotient of | #35291084, #35291087, #35291096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2499);