Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #483×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3336 |
342 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^82,f^c=fg,h^c=h^82814 conjugacy classes — view the full character table.
| maximal subgroup of | #3336×D83, C2×#24919829, #36282911, … |
| maximal normal subgroup of | #3336×D83, C2×#24919829, #36282911, … |
| maximal quotient of | #35420627, #35420633, #35422043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16876);