Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1370 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=ce,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1370×D83, C2×#24905532, #35315973, … |
| maximal normal subgroup of | #1370×D83, C2×#24905532, #35315973, … |
| maximal quotient of | #35291143, #35291145, #35291266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2579);