Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1413 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=f,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cf,d^b=def,e^b=eg,h^b=h^82,d^c=dfg,e^d=eg547 conjugacy classes — view the full character table.
| maximal subgroup of | #1413×D83, C2×#24905635, #35324762, … |
| maximal normal subgroup of | #1413×D83, C2×#24905635, #35324762, … |
| maximal quotient of | #35291794, #35291812, #35291943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2682);