Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1364 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^82,c^b=cf,d^b=def,f^b=fg,h^b=h^821177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1364×D83, C2×#24905519, #35315690, … |
| maximal normal subgroup of | #1364×D83, C2×#24905519, #35315690, … |
| maximal quotient of | #35291193, #35291591, #35292056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2566);