Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | H(3,𝔽4)×C173 ⋊ C2 |
| Sylow | C173 ⋊ #1655 |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^172,d^b=df,e^b=eg,d^c=dg,e^c=efg1654 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 3799);