Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #447×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3297 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=de,h^b=h^82,f^c=fg814 conjugacy classes — view the full character table.
| maximal subgroup of | #3297×D83, C2×#24919317, #36280883, … |
| maximal normal subgroup of | #3297×D83, C2×#24919317, #36280883, … |
| maximal quotient of | #35419825, #35420653, #35421591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16364);