Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #454×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3290 |
454 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,c^b=cg,d^b=de,e^b=eg,f^c=fg,e^d=eg,h^d=h^82685 conjugacy classes — view the full character table.
| maximal subgroup of | #3290×D83, C2×#24919242, #36280637, … |
| maximal normal subgroup of | #3290×D83, C2×#24919242, #36280637, … |
| maximal quotient of | #35395664, #35395700, #35395705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16289);