Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #501×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3163 |
340 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^c=h^82,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #3163×D83, C2×#24917990, #36274042, … |
| maximal normal subgroup of | #3163×D83, C2×#24917990, #36274042, … |
| maximal quotient of | #35404845, #35407761, #35407775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15037);