Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #453×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3288 |
464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,f^c=fg,e^d=eg,h^d=h^82682 conjugacy classes — view the full character table.
| maximal subgroup of | #3288×D83, C2×#24919224, #36280599, … |
| maximal normal subgroup of | #3288×D83, C2×#24919224, #36280599, … |
| maximal quotient of | #35393744, #35393749, #35393769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16271);