Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #479×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3108 |
390 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,h^b=h^82,f^c=fg,h^d=h^82817 conjugacy classes — view the full character table.
| maximal subgroup of | #3108×D83, C2×#24917548, #36272501, … |
| maximal normal subgroup of | #3108×D83, C2×#24917548, #36272501, … |
| maximal quotient of | #35404422, #35407358, #35407360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14595);