Finite Group DatabasebetaFinite Group Databasebeta| order | 24224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C757 ⋊ C4 |
| Sylow | C757 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6056 |
Polycyclic presentation:
2^5,757|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^87,c^b=ce,f^d=f^756959 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24224, 208);