Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C4×C4⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | (C2×C4×C4⋊(C3⋊D3))⋊C3 |
| Fitting | C2×C42×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×C4×D4 |
1599 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18366);