Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #441×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3120 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^82,f^c=fg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #3120×D83, C2×#24917675, #36272767, … |
| maximal normal subgroup of | #3120×D83, C2×#24917675, #36272767, … |
| maximal quotient of | #35404512, #35407478, #35407514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14722);