Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1420 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^82,c^b=ceg,d^b=dg,e^b=ef,f^b=fg928 conjugacy classes — view the full character table.
| maximal subgroup of | #1420×D83, C2×#24905656, #35324879, … |
| maximal normal subgroup of | #1420×D83, C2×#24905656, #35324879, … |
| maximal quotient of | #35291863, #35291968, #35292040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2703);