Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#3697⋊C3 |
| unambiguous semidirect product | (C4×#3697)⋊C3 |
| Fitting | C2×C42×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C4×#41 |
984 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #72268952, #72268958, C4×#41×AGL(1,ℤ/9) |
| maximal normal subgroup of | #72268952, #72268958, C4×#41×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18380);