Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #126×C173 ⋊ C4 |
| Sylow | C173 ⋊ #2373 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2768 |
Polycyclic presentation:
2^7,173|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^93,d^b=de,h^b=h^80,h^g=h^172652 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 21047);