Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #463×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3221 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^82,f^c=fg,h^d=h^82805 conjugacy classes — view the full character table.
| maximal subgroup of | #3221×D83, C2×#24918521, #36275813, … |
| maximal normal subgroup of | #3221×D83, C2×#24918521, #36275813, … |
| maximal quotient of | #35413786, #35414186, #35414990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15568);