Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #388×C173 ⋊ C2 |
| Sylow | C173 ⋊ C4×#124 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=g,b^2=f,c^2=e,d^2=g,b^a=be,c^a=cf,h^c=h^172,h^d=h^1722464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 7051);