Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C33 |
| direct product | C24×C3⋊(C3⋊Dic3) |
| derived, Sylow | C33 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C3⋊(C3⋊D3) |
| commutator, hypocenter | C33 | C24×C4 |
| Frattini | C2 | C24×C3⋊(C3⋊D3) |
| Fitting, socle, prime radical | C25×C33 | C2 |
| cosocle | C2×C33 | C25 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C25 | |
19068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1728 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47831);