Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #499×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3351 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^c=h^82,h^d=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #3351×D83, C2×#24920022, #36283158, … |
| maximal normal subgroup of | #3351×D83, C2×#24920022, #36283158, … |
| maximal quotient of | #35420811, #35420837, #35422134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17069);