Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | Q8 ⋊ #6875 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^5,2^3|a^3=d,b^3=c,c^3=e,f^2=h,g^2=h,b^a=bc,c^a=ce,f^a=fg,g^a=f,d^b=de^2,g^f=gh103 conjugacy classes — view the full character table.
| maximal subgroup of | SL(2,𝔽3)×#6875, #72276108 |
| maximal normal subgroup of | SL(2,𝔽3)×#6875 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 258);