Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #733⋊Q8 |
| Sylow | #733 ⋊ Q8 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^4|a^2=c,b^2=c,d^3=g^2,e^3=g^2,b^a=bc,d^a=d^2g,e^a=e^2g,f^a=fg^2,g^a=g^2,e^d=ef,f^d=fg43 conjugacy classes — view the full character table.
| maximal subgroup of | #13046758, #13046761, #13046817, … |
| maximal normal subgroup of | #13046758, #13046761, #13046817, … |
| maximal quotient of | (#733⋊C4)⋊C4, C4⋊(#733⋊C4), C2×#733⋊Q8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 188);