Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C173 ⋊ C2 |
| Sylow | C173 ⋊ #2929 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^d=h^1723496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 13199);